Stats Extra Credit Review #2

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

Which of the following is NOT a characteristic of the normal probability distribution?

The standard deviation must be 1

Sampling distributions describe the distribution of

the sample statistics

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. Students who made 60 or lower on the exam failed the course. What fraction of students failed the course?

.0043

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. What is the probability that the mean balance for the selected sample is below $390?

.0093

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. Students who made 60 or lower on the exam failed the course. 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?

.0168

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. What is the probability that a particular delivery will exceed one hour?

.1911

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)

.21

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)

.252

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)

.253

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. What is the probability that the mean balance for the selected sample is between $401 and $405?

.2874

The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 30 pounds. What is the probability of a player weighing more than 210 pounds?

.3694

The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 30 pounds. What fraction of players weigh between 165 and 200 pounds?

.3783

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 faction of students scored above 81?

.5

For the standard normal probability distribution, the area under the probability density function to the left of the mean is

.5

In a standard normal distribution, the probability that z is greater than zero is

.5

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. 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?

.5631

The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 30 pounds. What is the probability of a player weighing less than 210 pounds?

.6306

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. What is the probability that the mean balance for the selected sample is above $395?

.8804

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. What is the probability Professor Elderman's class of 36 students has a class average below 82?

.9088

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-bar 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? Find the required probability. (Round your solution to 4 decimal places)

.9123

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. What is the probability that a class of 36 students will have an average greater than 70 points on Professor Elderman's final exam?

.9962

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?

1.25

The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 30 pounds. 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

The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 30 pounds. What is the minimum weight of the middle 94% of the players?

143.5762

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. What is the value of the mean for the normal distribution you would use for approximation?

16.6

The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 30 pounds. What is the maximum weight of the bottom 10% of the players? Correct!

161.5535

The prices of condos in a city are normally distributed with a mean of $120,000 and a standard deviation of $35,000. Answer the following questions rounding your answers to 4 decimal places. 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?

164854.3

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-bar 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? 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 3 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?

2.375

The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 30 pounds. What is the minimum weight of the top 5% of the players?

249.3456

The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 30 pounds. What is the maximum weight of the middle 98% of the players?

269.7904

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. 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-bar, was calculated. The mean of the sampling distribution of x-bar is

490.4

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. This question is similar to the previous one but is phrased differently. 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.

52337.5

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.

54699.73

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?

576

The prices of condos in a city are normally distributed with a mean of $120,000 and a standard deviation of $35,000. Answer the following questions rounding your answers to 4 decimal places. 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?

58725.99

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. Students who made 60 or lower on the exam failed the course. 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

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-bar 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? What is the mean of the sampling distribution of x-bar?

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-bar is

81

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

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. 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?

Cannot be determined

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. What is the probability that a randomly selected student in the class will score greater than 70 points on Professor Elderman's final exam

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 approximately normal with the mean = 10 minutes and the standard error = .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

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. 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 conditions for approximation, np>=5 and N91-p)>=5, are not satisfied in this problem.

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. 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?

No, because conditions for approximation, np>=5 and n(1-p)>=5 are not satisfied in this problem.

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<=x<=3)

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 smaller than P(x<16)

The central limit theorem states that

Sample means of large-sized samples will be normally distributed regardless of the shape of their population distributions

Which of the following can be represented by a continuous random variable?

The number of defective light bulbs in a sample of five

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.

The picture is inconclusive. We need to perform calculations to answer this question.

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-bar 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? What is the shape of the sampling distribution of x-bar?

The sampling distribution of x-bar is normal because the sample size is >30 and the CLT applies in this case.

As the size of the sample increases,

The standard error of the mean decreases

How does the variance of the sample mean compare to the variance of the population?

The variance of the sample mean is smaller and, thus, suggests that averages have less variation than individual observations.

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. 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?

Yes, because conditions for approximation, np>=5 and n(1-p) >= 5, are satisfied in this problem.

A continuous random variable may assume

any value in an interval or collection of intervals

The center of a normal curve

is the median of the distribution

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

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-bar is

normal because the sample size is >=30

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-bar is

not possible to say because the sample size is 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

not possible to say because the sample size is too small to apply the CLT

The normal distribution can well approximate the binomial distribution as long as

np>=5, nq>=5

What is the relationship between the expected value of the sample mean and the expected value of the population?

sample mean (mean of x-bar) = population mean

A smaller standard deviation for the normal probability distribution results in a

skinnier curve that is tighter and taller around the mean

What is the relationship between the standard deviation of the sample mean and the population standard deviation?

standard deviation of the sample mean = population standard deviation/sqrt (sample size)

For a continuous random variable x, the probability density function f(x) represents

the height of the function at x

sampling distribution of x-bar is

the probability distribution of the sample mean

The standard deviation of the sampling distribution of x-bar (sample mean) is called

the standard error of the mean

For any continuous random variable, the probability that the random variable takes on exactly a specific value is

zero