ECON-E 370 Exam 2 Prep (HW4-5s, quizzes, quick checks)
What is the relationship between the standard deviation of the sample mean and the population standard deviation? σx¯=σ/(n−1) σx¯=σ/n σx¯=σ/sqrt(n−1) σx¯=σ/sqrt(n)
σx¯=σ/sqrt(n)
According to the website Zillow, the average market value of the homes in the Taylor's Mill neighborhood is $454,000 with a standard deviation of $34,000. What is the standard error of the mean for a random sample of 23 homes from this neighborhood? - $7,089.49 - $1,478.261 - $94,665.54 - Not possible to say because the sample size is less than 30 observations
$7,089.49
Exhibit: Standard Normal Distribution. Calculate the following for the standard normal distribution using Excel. Round your solutions to 4 decimal places. Hints: 1) it's easier to understand the question if you draw a picture; 2) recall that the standard normal distribution has the mean of 0 and the standard deviation of 1. What is the value of z0 if P(z ≤ z0) = 0.25?
-0.6745
Exhibit: Student Grades. A professor at a local university noted that the grades of her students were normally distributed with a mean of 81 and a standard deviation of 8. Students who made 60 or lower on the exam failed the course. What fraction of students failed the course?
0.0043
Exhibit: Checking Accounts. A bank has kept records of the checking balances of its customers and determined that the average daily balance of its customers is $400 with a standard deviation of $63. A random sample of 220 checking accounts is selected. You are interested in calculating the following probabilities below. For all answers below, do not round intermediate steps if any and round your final answer to 4 decimal places. What is the probability that the mean balance for the selected sample is below $390?
0.0093
Exhibit: Student Grades. A professor at a local university noted that the grades of her students were normally distributed with a mean of 81 and a standard deviation of 8. The professor has informed the class that students who scored over 98% on the exam (out of 100 points) demonstrated exceptional performance on the exam. What fraction of students fall into this category?
0.0168
In a restaurant, the proportion of people who order coffee with their dinner is 0.9. A random sample of 144 patrons of the restaurant is taken. What is the standard deviation of the sampling distribution of the proportion of people who order coffee with their dinner when a sample of 144 patrons is used? - 0.025 - 11.3842 - 3.6 - 0.0006
0.025
Exhibit Supplier Delivery Times. Supplier on-time delivery performance is critical to enabling the buyer's organization to meet its customer service commitments. Therefore, monitoring supplier delivery times is also critical. Based on a great deal of historical data, a manufacturer of personal computers finds for one of its just-in-time suppliers that the delivery times are random and approximately follow the normal distribution with the mean of 51.7 minutes and the standard deviation of 9.5 minutes. Answer the following questions rounding your final answers to 4 decimal places. To avoid rounding errors, please do not round intermediate steps in your calculations. What is the probability that the mean time of five deliveries will exceed one hour? Hint: You'd want to use "60 minutes" as the equivalent of one hour.
0.0254
Exhibit: Female Employees. According to a recent Catalyst Census, 16% of executive officers were women with companies that have company headquarters in the Midwest. A random sample of 174 executive officers from these companies was selected. What is the probability that more than 20% of this sample is comprised of female employees? The sequence of questions below will help you approach this problem. Compute the standard error of the proportion. Round your answer to 4 decimal places.
0.0278
According to IDC, Apple's share of the smartphone market was 20% during the 3rd quarter of 2011. A random sample of 115 smartphone users was selected and it was found that 20 of them are Apple users. The standard error of the proportion of Apple users in a sample of 115 smartphone users is - 0.0373 - 0.0157 - 0.0690 - 0.1016
0.0373
Exhibit: Standard Normal Distribution. Calculate the following for the standard normal distribution using Excel. Round your solutions to 4 decimal places. Hints: 1) it's easier to understand the question if you draw a picture; 2) recall that the standard normal distribution has the mean of 0 and the standard deviation of 1. What is the probability of obtaining a z value between -2.5 and -1.5?
0.0606
Exhibit: Female Employees. According to a recent Catalyst Census, 16% of executive officers were women with companies that have company headquarters in the Midwest. A random sample of 174 executive officers from these companies was selected. What is the probability that more than 20% of this sample is comprised of female employees? The sequence of questions below will help you approach this problem. Use the sampling distribution of the proportion to find the required probability. Round your answer to 4 decimal places. Hint: this requires Excel.
0.075
Exhibit: Standard Normal Distribution. Calculate the following for the standard normal distribution using Excel. Round your solutions to 4 decimal places. Hints: 1) it's easier to understand the question if you draw a picture; 2) recall that the standard normal distribution has the mean of 0 and the standard deviation of 1. What is the probability of obtaining a z value more than 1.25?
0.1056
Exhibit Supplier Delivery Times. Supplier on-time delivery performance is critical to enabling the buyer's organization to meet its customer service commitments. Therefore, monitoring supplier delivery times is also critical. Based on a great deal of historical data, a manufacturer of personal computers finds for one of its just-in-time suppliers that the delivery times are random and approximately follow the normal distribution with the mean of 51.7 minutes and the standard deviation of 9.5 minutes. Answer the following questions rounding your final answers to 4 decimal places. To avoid rounding errors, please do not round intermediate steps in your calculations. What is the probability that the mean time of two deliveries will exceed one hour? Hint: You'd want to use "60 minutes" as the equivalent of one hour.
0.1083
Exhibit Illegal Immigration. The U.S. unauthorized immigrant population rose rapidly from 1990 to 2007 before declining sharply for two years and stabilizing at 10.5 million in 2017. While its share has declined, California still accounts for 24% of the nation's estimated undocumented immigrant population. For all answers, do not round intermediate steps (if any) and round your final answer to 4 decimal places. Hint: all proportions in these calculations have to be represented as decimal fractions. In a sample of 50 illegal immigrants, what is the probability that the percentage of illegal immigrants who live in California is between 30% and 35%?
0.126
Exhibit: Female Employees. According to a recent Catalyst Census, 16% of executive officers were women with companies that have company headquarters in the Midwest. A random sample of 174 executive officers from these companies was selected. What is the probability that more than 20% of this sample is comprised of female employees? The sequence of questions below will help you approach this problem. What is the mean of the sampling distribution of the proportion of female executive officers?
0.16
Exhibit Supplier Delivery Times. Supplier on-time delivery performance is critical to enabling the buyer's organization to meet its customer service commitments. Therefore, monitoring supplier delivery times is also critical. Based on a great deal of historical data, a manufacturer of personal computers finds for one of its just-in-time suppliers that the delivery times are random and approximately follow the normal distribution with the mean of 51.7 minutes and the standard deviation of 9.5 minutes. Answer the following questions rounding your final answers to 4 decimal places. To avoid rounding errors, please do not round intermediate steps in your calculations. What is the probability that a particular delivery will exceed one hour? Hint: You'd want to use "60 minutes" as the equivalent to one hour because the distribution characteristics are expressed in minutes.
0.1911
According to IDC, Apple's share of the smartphone market was 20% during the 3rd quarter of 2011. A random sample of 115 smartphone users was selected and it was found that 20 of them are Apple users. What is the mean of the sampling distribution of the proportion of Apple users when a sample of 115 smartphone users is used? - 23 - 0.1739 - 0.2 - 20
0.2
Exhibit: Teacher's Salary. The salary of teachers in a particular school district is normally distributed with a mean of $40,000 and a standard deviation of $7,500. Knowing the distribution of salaries, the following probabilities were calculated: P(x≤45,000)=0.748; P(x≤53,000)=0.958. Find probabilities in the following questions relying on the cumulative probabilities above. Find the probability that a randomly selected teacher receives a salary greater than $45,000 but less than or equal to $53,000. (Do not round your answer)
0.21
Exhibit: Teacher's Salary. The salary of teachers in a particular school district is normally distributed with a mean of $40,000 and a standard deviation of $7,500. Knowing the distribution of salaries, the following probabilities were calculated: P(x≤45,000)=0.748; P(x≤53,000)=0.958. Find probabilities in the following questions relying on the cumulative probabilities above. Find the probability that a randomly selected teacher receives a salary of $45,000 or more. (Do not round your answer)
0.252
Exhibit: Teacher's Salary. The salary of teachers in a particular school district is normally distributed with a mean of $40,000 and a standard deviation of $7,500. Knowing the distribution of salaries, the following probabilities were calculated: P(x≤45,000)=0.748; P(x≤53,000)=0.958. Find probabilities in the following questions relying on the cumulative probabilities above. Find the probability that a randomly selected teacher receives a salary of more than $45,000. (Do not round your answer)
0.252
Exhibit: Checking Accounts. A bank has kept records of the checking balances of its customers and determined that the average daily balance of its customers is $400 with a standard deviation of $63. A random sample of 220 checking accounts is selected. You are interested in calculating the following probabilities below. For all answers below, do not round intermediate steps if any and round your final answer to 4 decimal places. What is the probability that the mean balance for the selected sample is between $401 and $405?
0.2874
Exhibit: Football Players. The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 30 pounds. Answer the following questions rounding your solutions to 4 decimal places. What is the probability of a player weighing more than 210 pounds?
0.3694
Exhibit: Football Players. The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 30 pounds. Answer the following questions rounding your solutions to 4 decimal places. What fraction of players weigh between 165 and 200 pounds?
0.3783
Exhibit: Student Grades. A professor at a local university noted that the grades of her students were normally distributed with a mean of 81 and a standard deviation of 8. What fraction of students scored above 81?
0.5
For the standard normal probability distribution, the area under the probability density function to the left of the mean is - 0.5 - any value between 0 to 1 - Cannot say exactly without knowing the value of the mean = 1
0.5
In a standard normal distribution, the probability that z is greater than zero is - 0.5 - at least 0.5 - 1.96 - 1
0.5
Exhibit: Checking Accounts. A bank has kept records of the checking balances of its customers and determined that the average daily balance of its customers is $400 with a standard deviation of $63. A random sample of 220 checking accounts is selected. You are interested in calculating the following probabilities below. For all answers below, do not round intermediate steps if any and round your final answer to 4 decimal places. Assuming that the population of the checking account balances is normally distributed, what is the probability that a randomly selected account has a balance of more than $390?
0.5631
A random sample of size 100 is taken from a population described by the proportion p = 0.60. What are the mean and the standard deviation of the sampling distribution of the sample proportion? - 0.600 and 0.049 - 0.060 and 0.049 - 0.600 and 0.0024 - 0.006 and 0.0024
0.600 and 0.049
Exhibit: Football Players. The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 30 pounds. Answer the following questions rounding your solutions to 4 decimal places. What is the probability of a player weighing less than 210 pounds?
0.6306
Exhibit Illegal Immigration. The U.S. unauthorized immigrant population rose rapidly from 1990 to 2007 before declining sharply for two years and stabilizing at 10.5 million in 2017. While its share has declined, California still accounts for 24% of the nation's estimated undocumented immigrant population. For all answers, do not round intermediate steps (if any) and round your final answer to 4 decimal places. Hint: all proportions in these calculations have to be represented as decimal fractions. In a sample of 50 illegal immigrants, what is the probability that more than 20% live in California?
0.7461
Exhibit: Standard Normal Distribution. Calculate the following for the standard normal distribution using Excel. Round your solutions to 4 decimal places. Hints: 1) it's easier to understand the question if you draw a picture; 2) recall that the standard normal distribution has the mean of 0 and the standard deviation of 1. Find the value of z such that the area to the left of z is 0.8.
0.8416
Exhibit: Checking Accounts. A bank has kept records of the checking balances of its customers and determined that the average daily balance of its customers is $400 with a standard deviation of $63. A random sample of 220 checking accounts is selected. You are interested in calculating the following probabilities below. For all answers below, do not round intermediate steps if any and round your final answer to 4 decimal places. What is the probability that the mean balance for the selected sample is above $395?
0.8804
In a restaurant, the proportion of people who order coffee with their dinner is 0.9. A random sample of 144 patrons of the restaurant is taken. What is the mean of the sampling distribution of the proportion of people who order coffee with their dinner when a sample of 144 patrons is used? - 129.6 - 0.9 - Not possible to say because the number of people who ordered coffee in the sample is not known - It is the same as p¯.
0.9
Exhibit Exam Scores. Professor Elderman has given the same multiple-choice final exam in his Principles of Microeconomics class for many years. After examining his records from the past 20 years, he finds that the scores have a mean of 78 points and a standard deviation of 18 points. Answer the following questions rounding your final answer to 4 decimal places. To avoid rounding errors, please do not round intermediate steps in your calculations. What is the probability Professor Elderman's class of 36 students has a class average below 82?
0.9088
Exhibit: Biology Class A biology class recently had an exam. The mean exam score was 79 points and the standard deviation of the exam score was 14 points. Let x¯ denote the sample average score for a sample of 40 exams. What is the probability that a random sample of 40 exams has an average score below 82 points? The sequence of questions below will help you approach this problem. Find the required probability. (Round your solution to 4 decimal places) Hint: This requires Excel. Think about what you need to use for the standard deviation inside the Excel function.
0.9123
Exhibit: Standard Normal Distribution. Calculate the following for the standard normal distribution using Excel. Round your solutions to 4 decimal places. Hints: 1) it's easier to understand the question if you draw a picture; 2) recall that the standard normal distribution has the mean of 0 and the standard deviation of 1. What is the probability of obtaining a z value less than 1.5?
0.9332
Exhibit Exam Scores. Professor Elderman has given the same multiple-choice final exam in his Principles of Microeconomics class for many years. After examining his records from the past 20 years, he finds that the scores have a mean of 78 points and a standard deviation of 18 points. Answer the following questions rounding your final answer to 4 decimal places. To avoid rounding errors, please do not round intermediate steps in your calculations. What is the probability that a class of 36 students will have an average greater than 70 points on Professor Elderman's final exam? - 0.5879 - Cannot be determined - 0.6716 - 0.9962
0.9962
Exhibit: Standard Normal Distribution. Calculate the following for the standard normal distribution using Excel. Round your solutions to 4 decimal places. Hints: 1) it's easier to understand the question if you draw a picture; 2) recall that the standard normal distribution has the mean of 0 and the standard deviation of 1. What is the value of z if the area between -z and z is 0.7?
1.0365
A nursery sells trees of different types and heights. These trees average 112 inches in height with a standard deviation of 14 inches. Suppose that 125 pine trees are sold for planting at City Hall. What is the standard deviation of the sample meanfor sample of 125 trees? - 3.74 - 1.25 - 14 - 1.56
1.25
Exhibit: Standard Normal Distribution. Calculate the following for the standard normal distribution using Excel. Round your solutions to 4 decimal places. Hints: 1) it's easier to understand the question if you draw a picture; 2) recall that the standard normal distribution has the mean of 0 and the standard deviation of 1. Find the value of z such that the area to the right of z is 0.05.
1.6449
Exhibit: Football Players. The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 30 pounds. Answer the following questions rounding your solutions to 4 decimal places. What is the minimum weight of the middle 95% of the players? (Please, use Excel to find the value rather than statistical tables to avoid rounding errors)
141.2011
Exhibit: Football Players. The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 30 pounds. Answer the following questions rounding your solutions to 4 decimal places. What is the minimum weight of the middle 94% of the players?
143.5762
Exhibit: Unemployment. According to the Bureau of Labor Statistics, 8.3% of the labor force was recently unemployed. A random sample of 200 employable adults was selected. For this Exhibit, assume that you are interested in approximating probabilities that the number of unemployed individuals falls into a specific interval using the normal probability distribution. Round your answers to 4 decimal places. What is the value of the mean for the normal distribution you would use for approximation?
16.6
Exhibit: Football Players. The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 30 pounds. Answer the following questions rounding your solutions to 4 decimal places. What is the maximum weight of the bottom 10% of the players?
161.5535
Exhibit: Condo Price. The prices of condos in a city are normally distributed with a mean of $120,000 and a standard deviation of $35,000. If 10% of the most expensive condos are subject to a luxury tax, what is the minimum price of condos that will be subject to the luxury tax?
164,854.3048
Exhibit: Biology Class A biology class recently had an exam. The mean exam score was 79 points and the standard deviation of the exam score was 14 points. Let x¯ denote the sample average score for a sample of 40 exams. What is the probability that a random sample of 40 exams has an average score below 82 points? The sequence of questions below will help you approach this problem. Compute the standard error of the mean. (Round your answer to 4 decimal places)
2.2136
Consider the following population which represents the number of pieces of junk mail that some individual "X" received during the month of February. 2 4 0 3 5 1 3 2 3 0 5 5 1 1 3 5 0 2 3 0 2 3 3 1 What is the mean of the sampling distribution of the mean number of junk mail for that person? - It can be anything. - A sample size is needed to determine the mean of the sampling distribution. - 2.375 - 57
2.375
Exhibit: Football Players. The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 30 pounds. Answer the following questions rounding your solutions to 4 decimal places. What is the minimum weight of the top 5% of the players?
249.3456
Exhibit: Football Players. The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 30 pounds. Answer the following questions rounding your solutions to 4 decimal places. What is the maximum weight of the middle 98% of the players?
269.7904
Exhibit: Unemployment. According to the Bureau of Labor Statistics, 8.3% of the labor force was recently unemployed. A random sample of 200 employable adults was selected. For this Exhibit, assume that you are interested in approximating probabilities that the number of unemployed individuals falls into a specific interval using the normal probability distribution. Round your answers to 4 decimal places. What is the value of the standard deviation for the normal distribution you would use for approximation?
3.9016
Suppose that the average math SAT score for full-time students enrolled at Madison College is 490.4 with a standard deviation of 21. A random sample of 9 students has been selected and a sample average math SAT score, x¯, was calculated. The mean of the sampling distribution of x¯ is - not possible to say because CLT does not apply -21 - 7 - 490.4
490.4
The sampling distribution of the proportion follows the normal distribution when values of np and nq are greater than or equal to - 0.05 - 30 - 5 - 30
5
Exhibit: Teacher's Salary. The salary of teachers in a particular school district is normally distributed with a mean of $40,000 and a standard deviation of $7,500. Knowing the distribution of salaries, the following probabilities were calculated: P(x≤45,000)=0.748; P(x≤53,000)=0.958. Find probabilities in the following questions relying on the cumulative probabilities above. Due to budget limitations, it has been decided that the teachers who are in the top 5% of the salaries would not get a raise. What is the salary level that divides the teachers into one group that gets a raise and one that doesn't? Choose an appropriate z-score for your calculations using the following information: P(z≤1.645)=0.95 P(z≤2.58)=0.995 P(z≤1.28)=0.9 Do not round your answer. It is expected that you can solve this question without Excel.
52,337.5
Exhibit: Teacher's Salary. The salary of teachers in a particular school district is normally distributed with a mean of $40,000 and a standard deviation of $7,500. Knowing the distribution of salaries, the following probabilities were calculated: P(x≤45,000)=0.748; P(x≤53,000)=0.958. Find probabilities in the following questions relying on the cumulative probabilities above. Due to budget limitations, it has been decided that the teachers who are in the top 2.5% of the salaries would not get a raise. What is the salary level that divides the teachers into one group that gets a raise and one that doesn't? (Do not round your answer). Assume that the value of z0 such that P(z≥z0)=0.025 is equal to 1.96.
54,700
The population standard deviation is measured 120. A sample of 25 observations is taken from the population. What is the variance of the sampling distribution of the mean for this sample? - 24 - 23.04 - 576 - 120
576
Exhibit: Condo Price. The prices of condos in a city are normally distributed with a mean of $120,000 and a standard deviation of $35,000. The city government exempts the cheapest 4% of the condos from city taxes. What is the maximum price of the condos that will be exempt from city taxes?
58,725.9875
Suppose that, on average, electricians earn approximately µ = $54,000 per year in the United States. Assume that the distribution for electricians' yearly earnings is normally distributed and that the standard deviation is σ = $12,000. Given a sample of four electricians, what is the standard deviation for the sampling distribution of the sample mean? - 54000 - 6000 - 12000 - 36000
6000
A population has a mean of 75 and a standard deviation of 8. A random sample of 800 is selected. The mean of the sampling distribution is - 75 - 800 - none of the suggested alternatives is correct - 8
75
Exhibit: Student Grades. A professor at a local university noted that the grades of her students were normally distributed with a mean of 81 and a standard deviation of 8. If 69.5 percent of the students received grades of C or better, what is the minimum score of those who received C's?
76.9194
Exhibit: Biology Class A biology class recently had an exam. The mean exam score was 79 points and the standard deviation of the exam score was 14 points. Let x¯ denote the sample average score for a sample of 40 exams. What is the probability that a random sample of 40 exams has an average score below 82 points? The sequence of questions below will help you approach this problem. What is the mean of the sampling distribution of x¯
79
Random samples of size 200 are taken from a population with the mean and standard deviation equal to 81 and 18, respectively. The distribution of the population is unknown. The mean of the sampling distribution of x¯ is - not enough information to determine - 18 - 200 - 81
81
Exhibit: Student Grades. A professor at a local university noted that the grades of her students were normally distributed with a mean of 81 and a standard deviation of 8. The professor has informed the class that 7.93 percent of her students received grades of A. What is the minimum score needed to receive a grade of A?
92.2784
The starting salaries of individuals with an MBA degree are normally distributed with a mean of $40,000 and a standard deviation of $5,000. How would you calculate the probability that a randomly selected individual with an MBA degree will get a starting salary above $35,000 in Excel? 1. =NORM.INV(35000,40000,5000) 2. =1-NORM.DIST(35000,40000,5000,FALSE) 3. =NORM.DIST(35000,40000,5000,TRUE) 4. =1-NORM.DIST(35000,40000,5000,TRUE)
=1-NORM.DIST(35000,40000,5000,TRUE)
The starting salaries of individuals with an MBA degree are normally distributed with a mean of $40,000 and a standard deviation of $5,000. How would you calculate the probability that a randomly selected individual with an MBA degree will get a starting salary below $35,000 in Excel? 1. =NORM.DIST(35000,40000,5000,TRUE) 2. =NORM.DIST(35000,40000,5000,FALSE) 3. =1-NORM.DIST(35000,40000,5000,TRUE) 4. =NORM.DIST(34999,40000,5000,TRUE)
=NORM.DIST(35000,40000,5000,TRUE)
The starting salaries of individuals with an MBA degree are normally distributed with a mean of $40,000 and a standard deviation of $5,000. How would you calculate the starting salary of bottom 5% of individuals with an MBA degree in Excel? 1. =NORM.INV(0.95,40000,5000) 2. =NORM.DIST(0.05,40000,5000,TRUE) 3. =NORM.INV(0.05,40000,5000) 4. =1-NORM.INV(0.05,40000,5000)
=NORM.INV(0.05,40000,5000)
Exhibit Exam Scores. Professor Elderman has given the same multiple-choice final exam in his Principles of Microeconomics class for many years. After examining his records from the past 20 years, he finds that the scores have a mean of 78 points and a standard deviation of 18 points. Answer the following questions rounding your final answer to 4 decimal places. To avoid rounding errors, please do not round intermediate steps in your calculations. What is the probability that a class of 15 students will have a class average greater than 70 points on Professor Elderman's final exam? - 0.7031 - 0.6716 - 0.9576 - Cannot be determined
Cannot be determined
Exhibit Exam Scores. Professor Elderman has given the same multiple-choice final exam in his Principles of Microeconomics class for many years. After examining his records from the past 20 years, he finds that the scores have a mean of 78 points and a standard deviation of 18 points. Answer the following questions rounding your final answer to 4 decimal places. To avoid rounding errors, please do not round intermediate steps in your calculations. What is the probability that a randomly selected student in the class will score greater than 70 points on Professor Elderman's final exam? - 0.6716 - 0.5879 - Cannot be determined - 0.9962
Cannot be determined
For air travelers, one of the biggest complaints is of the waiting time between when the airplane taxis away from the terminal until the flight takes off. This waiting time is known to have a right skewed distribution with a mean of 10 minutes and a standard deviation of 8 minutes. Suppose 100 fights have been randomly sampled. Describe the sampling distribution of the mean waiting time between when the airplane taxis away from the terminal until the flight takes off for these 100 flights. - Distribution is right skewed with the mean = 10 minutes and the standard error = 8 minutes - Distribution is approximately normal with the mean = 10 minutes and the standard error = 0.8 minutes - Distribution is approximately normal with the mean = 10 minutes and the standard error = 8 minutes - Distribution is right skewed with the mean = 10 minutes and the standard error = 0.8 minutes
Distribution is approximately normal with the mean = 10 minutes and the standard error = 0.8 minutes
You are considering the risk return profile of two mutual funds for investment. The relatively risky fund (Fund A) promises an expected return of 8% with a standard deviation of 14%. The relatively less risky fund (Fund B) promises an expected return and standard deviation of 4% and 5%, respectively. Assume that the returns are approximately normally distributed. Which mutual fund has a higher probability of earning a return above 8%? It is expected that you can answer this question without calculations using a picture only. - Fund A and Fund B have equal returns - Fund A - Fund B - The picture is inconclusive. We need to perform calculations to answer this question
Fund A
Exhibit: Unemployment. According to the Bureau of Labor Statistics, 8.3% of the labor force was recently unemployed. A random sample of 200 employable adults was selected. For this Exhibit, assume that you are interested in approximating probabilities that the number of unemployed individuals falls into a specific interval using the normal probability distribution. Round your answers to 4 decimal places. Assume that the conditions of the problem were different and, according to the Bureau of Labor Statistics, only 1.5% of the labor force was recently unemployed. You take a sample of 200 individuals. Suppose again that you are going to approximate a probability that exactly 12 people are unemployed in the sample, P(x = 12), using the normal distribution. Do you expect that approximated probability will be close to the actual probability that 12 individuals are unemployed in the sample? How do you know? - Yes, because conditions for approximation, np ≥ 5 and n(1 - p) ≥ 5, are satisfied in this problem. - Yes, because the normal probability distribution can be used to calculate any probability. - No, because the distribution for the number of unemployed in the sample is not known. - No, because conditions for approximation, np ≥ 5 and n(1 - p) ≥ 5, are not satisfied in this problem.
No, because conditions for approximation, np ≥ 5 and n(1 - p) ≥ 5, are not satisfied in this problem.
Exhibit: Unemployment. According to the Bureau of Labor Statistics, 8.3% of the labor force was recently unemployed. A random sample of 200 employable adults was selected. For this Exhibit, assume that you are interested in approximating probabilities that the number of unemployed individuals falls into a specific interval using the normal probability distribution. Round your answers to 4 decimal places. Let's once again assume that the conditions of the problem were different and 99% of the labor force was recently unemployed (this is not a realistic number, but let's assume it was the case). You take a sample of 200 individuals. Suppose that you are going to approximate a probability that exactly 194 people are unemployed in the sample, P(x = 194), using the normal distribution. Do you expect that approximated probability will be close to the actual probability that 194 individuals are unemployed in the sample? How do you know? - No, because the distribution for the number of unemployed in the sample is not known. - Yes, because conditions for approximation, np ≥ 5 and n(1 - p) ≥ 5, are satisfied in this problem. - No, because conditions for approximation, np ≥ 5 and n(1 - p) ≥ 5, are not satisfied in this problem. - Yes, because the number we are interested in is close to the sample size.
No, because conditions for approximation, np ≥ 5 and n(1 - p) ≥ 5, are not satisfied in this problem.
Exhibit: Female Employees. According to a recent Catalyst Census, 16% of executive officers were women with companies that have company headquarters in the Midwest. A random sample of 174 executive officers from these companies was selected. What is the probability that more than 20% of this sample is comprised of female employees? The sequence of questions below will help you approach this problem. What is the shape of the sampling distribution of the proportion? - It cannot be determined based on a given information. - The shape of the sampling distribution distribution of the proportion is the same as the distribution of the population. - Normal because n > 30. - Normal (or can be approximated by a normal) because np ≥ 5 and nq ≥ 5.
Normal (or can be approximated by a normal) because np ≥ 5 and nq ≥ 5.
It is known that the length of a certain product x is normally distributed with µ = 12 inches. How does the probability P(x>16) compare to P(x<16)? - P(x>16) is greater than P(x<16) - P(x>16) is smaller than P(x<16) - P(x>16) is the same as P(x<16) - No comparison can be made with the given information
P(x>16) is smaller than P(x<16)
If x has a normal distribution with µ = 10 and σ = 5, then the probability P(−15≤x≤25) can be expressed in terms of a standard normal variable z as - P(5≤z≤−3) - P(−5≤z≤−3) - P(−5≤z≤3) - P(−5≤z≤5)
P(−5≤z≤3)
What justifies the use of the normal distribution for the sampling distribution of the proportion? - The ability of the normal distribution to approximate the binomial distribution under appropriate conditions - The sample size greater than 30 observations - The normally distributed population data - The large population size
The ability of the normal distribution to approximate the binomial distribution under appropriate conditions
Which of the following can be represented by a continuous random variable? - The score of a randomly selected student on a five-question multiple-choice quiz - The number of defective light bulbs in a sample of five - The number of arrivals to a drive-through bank window in a four-hour period - The height of college students
The height of college students
You are considering the risk return profile of two mutual funds for investment. The relatively risky fund (Fund A) promises an expected return of 8% with a standard deviation of 14%. The relatively less risky fund (Fund B) promises an expected return and standard deviation of 4% and 5%, respectively. Assume that the returns are approximately normally distributed. Which mutual fund has a lower probability of negative return (below 0%)? It is expected that you can answer this question without calculations using a picture only. - Fund A and Fund B have equal returns - Fund A - Fund B - The picture is inconclusive. We need to perform calculations to answer this question
The picture is inconclusive. We need to perform calculations to answer this question
Exhibit Supplier Delivery Times. Supplier on-time delivery performance is critical to enabling the buyer's organization to meet its customer service commitments. Therefore, monitoring supplier delivery times is also critical. Based on a great deal of historical data, a manufacturer of personal computers finds for one of its just-in-time suppliers that the delivery times are random and approximately follow the normal distribution with the mean of 51.7 minutes and the standard deviation of 9.5 minutes. Answer the following questions rounding your final answers to 4 decimal places. To avoid rounding errors, please do not round intermediate steps in your calculations. What enables you to calculate the answer to the previous question? I.e. why you could numerically solve for the probability that a particular delivery will exceed one hour? - The probability in question is calculated from the population distribution of delivery times. The population distribution of delivery times is normal which enables us to use the normal distribution and the population standard deviation in the calculations. - These calculations are invalid. The probability in question should be calculated from the sampling distribution of the mean delivery times. However, the sample size is not given and no probability should be calculated. - We always use the normal distribution for the probability calculations with the sampling distribution of the mean. - The probability in question is calculated from the sampling distribution of the mean delivery times. The sampling distribution of the mean is normal which enables us to use the normal distribution and the standard error of the mean in the calculations.
The probability in question is calculated from the population distribution of delivery times. The population distribution of delivery times is normal which enables us to use the normal distribution and the population standard deviation in the calculations.
Exhibit Supplier Delivery Times. Supplier on-time delivery performance is critical to enabling the buyer's organization to meet its customer service commitments. Therefore, monitoring supplier delivery times is also critical. Based on a great deal of historical data, a manufacturer of personal computers finds for one of its just-in-time suppliers that the delivery times are random and approximately follow the normal distribution with the mean of 51.7 minutes and the standard deviation of 9.5 minutes. Answer the following questions rounding your final answers to 4 decimal places. To avoid rounding errors, please do not round intermediate steps in your calculations. What enables you to calculate the answer to the previous question? I.e. why you could numerically solve for the probability that the mean time of two deliveries will exceed one hour? - The probability in question is calculated from the population distribution of delivery times. The population distribution of delivery times is normal which enables us to use the normal distribution and the population standard deviation in the calculations. - We always use the normal distribution for probability calculations with the sampling distribution of the mean. - These calculations are invalid. The probability in question is calculated from the sampling distribution of the mean delivery times. However, the sample size is too small to apply the CLT and no probability should be calculated. - The probability in question is calculated from the sampling distribution of the mean delivery times. The sampling distribution of the mean is normal due to the fact that delivery times follow the normal distribution. This enables us to use normal distribution and the standard error of the mean in the calculations.
The probability in question is calculated from the sampling distribution of the mean delivery times. The sampling distribution of the mean is normal due to the fact that delivery times follow the normal distribution. This enables us to use normal distribution and the standard error of the mean in the calculations.
Exhibit Supplier Delivery Times. Supplier on-time delivery performance is critical to enabling the buyer's organization to meet its customer service commitments. Therefore, monitoring supplier delivery times is also critical. Based on a great deal of historical data, a manufacturer of personal computers finds for one of its just-in-time suppliers that the delivery times are random and approximately follow the normal distribution with the mean of 51.7 minutes and the standard deviation of 9.5 minutes. Answer the following questions rounding your final answers to 4 decimal places. To avoid rounding errors, please do not round intermediate steps in your calculations. Comparing the probability that the mean time of two and five deliveries will exceed one hour, which one is smaller? Why? Hint: Think about this question intuitively or use a picture without any calculations. Then, compare your answer with the calculated probabilities. Your intuition should be confirmed by the numbers you calculated. - The probability that the mean time of five deliveries will exceed one hour is smaller. This is due to the fact that the delivery times show more variation with larger sample size. - The probability that the mean time of five deliveries will exceed one hour is smaller. This is due to the fact that the sample size is larger which reduces the standard error of the mean and makes the tail probability smaller. - The probability that the mean time of two deliveries will exceed one hour is smaller. This is due to the fact that the standard error of the mean decreases as the sample size decreases. - The probability that the mean time of two deliveries will exceed one hour is smaller. This is due to the fact that the sample size is smaller which increases the standard error of the mean and makes the probability smaller.
The probability that the mean time of five deliveries will exceed one hour is smaller. This is due to the fact that the sample size is larger which reduces the standard error of the mean and makes the tail probability smaller.
What can be concluded about the sampling distribution of the mean if the population data is known to be normally distributed? - The sampling distribution of the mean is normally distributed only if the population distribution is not too skewed. - The sampling distribution of the mean is normally distributed only if the sample size consists of 30 or more observations. - The sampling distribution of the mean is normally distributed only if the sample size consists of 50 or more observations. - The sampling distribution of the mean is normally distributed for any sample size.
The sampling distribution of the mean is normally distributed for any sample size.
Exhibit: Biology Class A biology class recently had an exam. The mean exam score was 79 points and the standard deviation of the exam score was 14 points. Let x¯ denote the sample average score for a sample of 40 exams. What is the probability that a random sample of 40 exams has an average score below 82 points? The sequence of questions below will help you approach this problem. What is the shape of the sampling distribution of x¯? - The sampling distribution of x¯ can be any distribution because the population distribution is not specified here. Nevertheless, it does not affect the calculation of the probability in this problem. - The sampling distribution of x¯ is normal because the sample size is >30 and the CLT applies in this case. - The sampling distribution of x¯ is not normal because the population standard deviation is below 30. - The sampling distribution of x¯ is not known as the population distribution is not known in this problem.
The sampling distribution of x¯ is normal because the sample size is >30 and the CLT applies in this case.
How does the variance of the sample mean compare to the variance of the population? - The variance of the sample mean is larger and, thus, suggests that averages have more variation than individual observations. - The variance of the sample mean is smaller and, thus, suggests that averages have less variation than individual observations. - The variance of the sample mean is larger and, thus, suggests that averages have less variation than individual observations. - The variance of the sample mean is smaller and, thus, suggests that averages have more variation than individual observations.
The variance of the sample mean is smaller and, thus, suggests that averages have less variation than individual observations.
Exhibit: Unemployment. According to the Bureau of Labor Statistics, 8.3% of the labor force was recently unemployed. A random sample of 200 employable adults was selected. For this Exhibit, assume that you are interested in approximating probabilities that the number of unemployed individuals falls into a specific interval using the normal probability distribution. Round your answers to 4 decimal places. Suppose you are going to approximate a probability that exactly 12 people are unemployed in the sample, P(x = 12), using the normal distribution. Do you expect that approximated probability will be close to the actual probability that 12 individuals are unemployed in the sample? How do you know? - No, because the distribution of the number of unemployed in the sample is not known. - Yes, because conditions for approximation, np ≥ 5 and n(1 - p) ≥ 5, are satisfied in this problem. - No, because the distribution of the number of unemployed in the sample is discrete. - Yes, because the normal probability distribution can be used to calculate any probability.
Yes, because conditions for approximation, np ≥ 5 and n(1 - p) ≥ 5, are satisfied in this problem.
A normal distribution with a mean of 0 and a standard deviation of 1 is called - an ordinary normal curve - a standard normal distribution - a probability density function - None of the suggested alternatives is correct
a standard normal distribution
A continuous random variable may assume - only fractional values in an interval or collection of intervals - only integer values in an interval or collection of intervals - any value in an interval or collection of intervals - only the positive integer values in an interval
any value in an interval or collection of intervals
A continuous random variable may assume - only the positive integer values in an interval - only fractional values in an interval or collection of intervals - any value in an interval or collection of intervals - only integer values in an interval or collection of intervals
any value in an interval or collection of intervals
Samples of four people were asked whether gun laws should be more stringent. Respondents had a choice to answer "yes" or "no." The sampling distribution of the proportion of people who respond "yes" for the samples of 4 individuals is - normal - not possible to say because the sample size it too small - binomial because the number of people who respond "yes" has the binomial distribution - not possible to say because the population distribution is not known
binomial because the number of people who respond "yes" has the binomial distribution
For a continuous random variable x, the probability density function f(x) represents - height of the function at x - area under the curve at x - probability at a given value of x - area under the curve to the right of x
height of the function at x
The probability that a continuous random variable takes any specific value - is very close to 1 - is at least 0.5 - is equal to zero - depends on the probability density function
is equal to zero
The center of a normal curve is - cannot be negative - always equal to zero - is the standard deviation - is the mean of the distribution
is the mean of the distribution
The center of a normal curve - is the standard deviation - is always equal to zero - cannot be negative - is the median of the distribution
is the median of the distribution
What is the relationship between the mean of the sampling distribution of the mean and the mean of the population? - mu_xbar = mu/SQRT(n) - mu_xbar = mu - mu_xbar = SQRT(mu) - mu_xbar = mu/n
mu_xbar = mu
The battery life of the iPhone is normally distributed with the mean of 6.0 hours and the standard deviation 1.5 hours. A random sample of 17 iPhones is taken. The sampling distribution of the sample means for the battery life is - normal - can be any distribution - may or may not be normal - not possible to say because the sample size it too small
normal
A simple random sample of 56 observations was taken from a large population. The sample mean and the standard deviation were determined to be 36 and 10, respectively. The sampling distribution of x¯ is - normal because the population is large - not possible to say because the population distribution is not known - normal because the sample size is ≥30 - not possible to say because the sample size it too small
normal because the sample size is ≥30
A random sample of 130 mortgages in the state of Mississippi was randomly selected. From this sample, 20 were found to be delinquent on their current payment. What is the mean of the sampling distribution of the proportion of delinquent payments? - not possible to say because the population proportion is not known - not possible to say because the population distribution is not normal - 0.1538 - not possible to say because the sample size it too small
not possible to say because the population proportion is not known
According to the website Zillow, the average market value of the homes in the Taylor's Mill neighborhood is $454,000 with a standard deviation of $34,000. A random sample of 23 homes from this neighborhood was selected. The sampling distribution of x¯ is - the same as the distribution of market value of the homes in the Taylor's Mill neighborhood - normal - not possible to say because the sample size it too small - the same as the distribution of market value of the homes in the selected sample
not possible to say because the sample size it too small
The national average price for regular gasoline in February 2022 was reported to be $5.45 per gallon with a standard deviation of $0.83. A random sample of 25 gas stations was taken. The shape of the sampling distribution of the sample mean for the gasoline price is - the same as the population distribution of the gasoline price - normal - not possible to say because the sample size it too small to apply the CLT - not possible to say because the population standard deviation is too small
not possible to say because the sample size it too small to apply the CLT
What conditions must be met for the sampling distribution of the proportion to be normal? - Either np ≥ 5 or nq ≥ 5 - Population distribution should be normal - n ≥ 30 - np ≥ 5 and nq ≥ 5
np ≥ 5 and nq ≥ 5
The normal distribution can well approximate the binomial distribution as long as - np≥5 - np≥5,nq≥5 - nq≥5 - Approximation of the binomial distribution with the normal distribution always works well
np≥5,nq≥5
The function that defines the probability distribution of a continuous random variable is a - probability density function - uniform function - normal function - either normal or uniform depending on the situation
probability density function
Sampling distribution of x¯ is the - means of sample means - means of the population - mean of the sample - probability distribution of the sample mean
probability distribution of the sample mean
The Central Limit Theorem (CLT) states that the - sample means of large-sized samples will be normally distributed only for normally distributed populations - sample means of any samples will be normally distributed regardless of the shape of their population distributions - sample means of large-sized samples will be normally distributed regardless of the shape of their population distributions - sample means of any samples will be normally distributed only for normally distributed populations
sample means of large-sized samples will be normally distributed regardless of the shape of their population distributions
The probability distribution of all possible values of the sample proportion is the - sampling distribution of x¯ - sampling distribution of p - sampling distribution of p¯ - same as p¯, since it considers all possible values of the sample proportion
sampling distribution of p¯
What is the relationship between the standard deviation of the sample mean and the population standard deviation? - sigma_xbar = sigma/SQRT(n-1) - sigma_xbar = sigma/SQRT(n) - sigma_xbar = sigma - sigma_xbar = sigma/(n-1)
sigma_xbar = sigma/SQRT(n)
A smaller standard deviation for the normal probability distribution results in a - skinnier curve that is more spread out around the mean and not as tall - fatter curve that is more spread out around the mean and not as tall - fatter curve that is tighter and taller around the mean - skinnier curve that is tighter and taller around the mean
skinnier curve that is tighter and taller around the mean
Which of the following can be represented by a continuous random variable? - the number of typos found in the modules of this course - speed of automobiles on a highway - the number of defective light bulbs in a sample of five - the score of a randomly selected student on a five-question multiple-choice quiz
speed of automobiles on a highway
Which of the following is NOT a characteristic of the normal probability distribution? - the mean of the distribution can be negative, zero, or positive - the distribution is symmetrical - the mean, median, and the mode are equal - standard deviation must be 1
standard deviation must be 1
As the sample size n increases, the 1. standard deviation of the population decreases 2. standard error of the mean increases 3. standard error of the mean decreases 4. population mean increases
standard error of the mean decreases
Sampling distribution of x_bar is - the probability distribution of the population mean - the probability distribution of the sample mean - the mean of the sample - all possible values of the sample mean
the probability distribution of the sample mean
According to the Central Limit Theorem, the distribution of the sample means is normal if - the underlying population is normal - the sample size is large - the standard deviation of the population is known - both the underlying population is normal and the sample size is large are correct
the sample size is large not be both because... For any sample size n, the sampling distribution of the mean is normal if the population from which the sample is drawn is normally distributed. There is no need for the Central Limit Theorem in these instances. When the underlying distribution is unknown and sample size is large enough (n ≥ 30), the Central Limit Theorem allows us to assume normality.
Sampling distributions describe the distribution of - both the population parameters and the sample statistics - the population parameters - neither the parameters nor the statistics - the sample statistics
the sample statistics
The standard deviation of the sampling distribution of x¯ is called - the mean deviation - the central variation - the standard error of the mean - the standard error of the population mean
the standard error of the mean
As the size of the sample increases, - the sampling error increases - the population standard deviation decreases - the standard error of the mean decreases - the sampling distribution becomes wider
the standard error of the mean decreases
Larger values of the standard deviation result in a normal curve that is - shifted to the right - wider and flatter - narrower and more peaked - shifted to the left
wider and flatter
For any continuous random variable, the probability that the random variable takes on exactly a specific value is - 0.5 - zero - one - any value between 0 and 1
zero
What is the relationship between the expected value of the sample mean and the expected value of the population? - μx¯= sqrt(μ) - μx¯=μ/n - μx¯=μ/sqrt(n) - μx¯=μ
μx¯=μ
