Exam 2
An analyst estimates that the year-end price of a stock has the following probabilities: StockPrice Probability $80 0.10 $85 0.30 $90 0.40 $95 0.20 The stock's expected price at the end of the year is _______.
$88.50
Consider the following probability distribution. xi P(X = xi) -2 0.2 -1 0.1 0 0.3 1 0.4 The expected value and variance are _____ and ______, respectively.
-0.1; 1.29
According to the Department of Transportation, 27% of domestic flights were delayed in the last year at JFK airport. Five flights are randomly selected at JFK. What is the probability that all five flights are delayed?
0.0014
According to the Bureau of Labor Statistics it takes an average of 28 weeks for young workers to find a new job. Assume that the probability distribution is normal and that the standard deviation is two weeks. Use an appropriate normal transformation to calculate the probability that 32 young workers average less than 27 weeks to find a job.
0.0023
According to the Bureau of Labor Statistics it takes an average of 27 weeks for young workers to find a new job. Assume that the probability distribution is normal and that the standard deviation is two weeks. Use an appropriate normal transformation to calculate the probability that 31 young workers average less than 26 weeks to find a job.
0.0027
It is known that 8% of the calculators shipped from a particular factory are defective. What is the probability that exactly three of five chosen calculators are defective?
0.0043
Super Bowl XLVI was played between the New York Giants and the New England Patriots in Indianapolis. Due to a decade-long rivalry between the Patriots and the city's own team, the Colts, most Indianapolis residents were rooting heartily for the Giants. Suppose that 90% of Indianapolis residents wanted the Giants to beat the Patriots. Use an appropriate normal transformation to calculate the probability that from a sample of 200 Indianapolis residents, fewer than 170 were rooting for the Giants in Super Bowl XLIV
0.0091
According to the Bureau of Labor Statistics it takes an average of 16 weeks for young workers to find a new job. Assume that the probability distribution is normal and that the standard deviation is two weeks. Use an appropriate normal transformation to calculate the probability that 20 young workers average less than 15 weeks to find a job.
0.0225
A random sample of size 36 is taken from a population with mean µ = 17 and standard deviation σ = 6. What is the probability that the sample mean is less than 15?
0.0228
It is known that 12% of the calculators shipped from a particular factory are defective. What is the probability that exactly three of six chosen calculators are defective?
0.0236
Forty-four percent of consumers with credit cards carry balances from month to month. Four consumers with credit cards are randomly selected. What is the probability that all consumers carry a credit card balance?
0.0375
A random sample of size 49 is taken from a population with mean µ = 14 and standard deviation σ = 4. What is the probability that the sample mean is greater than 15?
0.0401
The probability P(Z < −1.28) is closest to ______.
0.10
Suppose the round-trip airfare between Boston and Orlando follows the normal probability distribution with a mean of $387.20 and a standard deviation of $68.50. What is the probability that a randomly selected airfare between Boston and San Francisco will be less than $300?
0.1015
According to the 2011 Gallup daily tracking polls (www.gallup.com, February 3, 2012), Mississippi is the most conservative U.S. state, with 56.2 percent of its residents identifying themselves as conservative. What is the probability that at least 50 respondents of a random sample of 100 Mississippi residents do not identify themselves as conservative?
0.1056
According to geologists, the San Francisco Bay Area experiences five earthquakes with a magnitude of 6.5 or greater every 100 years. What is the probability that no earthquakes with a magnitude of 6.5 or greater will strike the San Francisco Bay Area in the next 40 years?
0.1353
A random sample of 49 cast aluminium pots is taken from a production line once every day. The number of defective pots is counted. The proportion of defective pots has been closely examined in the past and is believed to be 0.05. What are the upper and lower control limits for the
0.1434 and -0.0
An analyst is forecasting net income for Excellence Corporation for the next fiscal year. Her low-end estimate of net income is $246,000, and her high-end estimate is $331,000. Prior research allows her to assume that net income follows a continuous uniform distribution. The probability that net income will be greater than or equal to $318,500 is ______.
0.147
On a particular busy section of the Garden State Parkway in New Jersey, police use radar guns to detect speeding drivers. Assume the time that elapses between successive speeders is exponentially distributed with the mean of 15 minutes. What is the probability of a waiting time in excess of 25 minutes between successive speeders?
0.1889
Suppose the average price of gasoline for a city in the United States follows a continuous uniform distribution with a lower bound of $3.50 per gallon and an upper bound of $3.80 per gallon. What is the probability a randomly chosen gas station charges more than $3.70 per gallon?
0.333
It is known that 10% of the calculators shipped from a particular factory are defective. What is the probability that at least one in a random sample of four calculators is defective?
0.3439
Patients scheduled to see their primary care physician at a particular hospital wait, on average, an additional eight minutes after their appointment is scheduled to start. Assume the time that patients wait is exponentially distributed. What is the probability a randomly selected patient will see the doctor within five minutes of the scheduled time?
0.4647
On a particular busy section of the Garden State Parkway in New Jersey, police use radar guns to detect speeding drivers. Assume the time that elapses between successive speeders is exponentially distributed with the mean of 15 minutes. What is the probability of a waiting time less than 10 minutes between successive speeders?
0.4866
A random sample of size 100 is taken from a population described by the proportion p = 0.60. Use an appropriate normal transformation to calculate the probability that the sample proportion is between 0.55 and 0.62.
0.5052
Chauncey Billups, a current shooting guard for the Los Angeles Clippers, has a career free-throw percentage of 89.4%. Suppose he shoots six free throws in tonight's game. What is the probability that Billups makes all six free throws?
0.5105
Suppose the round-trip airfare between Boston and Orlando follows the normal probability distribution with a mean of $387.20 and a standard deviation of $68.50. What is the probability that a randomly selected airfare between Boston and San Francisco will be between $325 and $425?
0.5275
Consider the following cumulative distribution function for the discrete random variable X. x 1 2 3 4 P(X ≤ x) 0.30 0.44 0.72 1.00 What is the probability that X is greater than 2?
0.56
Suppose the average price of gasoline for a city in the United States follows a continuous uniform distribution with a lower bound of $4.50 per gallon and an upper bound of $4.90 per gallon. What is the probability a randomly chosen gas station charges less than $4.75 per gallon?
0.625
The labor force participation rate is the number of people in the labor force divided by the number of people in the country who are of working age and not institutionalized. The BLS reported in February 2012 that the labor force participation rate in the United States was 63.7%. A marketing company asks 120 working-age people if they either have a job or are looking for a job, or, in other words, whether they are in the labor force. What are the expected value and the standard error for a labor participation rate in the company's sample?
0.637 and 0.0439
The labor force participation rate is the number of people in the labor force divided by the number of people in the country who are of working age and not institutionalized. The BLS reported in February 2012 that the labor force participation rate in the United States was 65.2%. A marketing company asks 110 working-age people if they either have a job or are looking for a job, or, in other words, whether they are in the labor force. What are the expected value and the standard error for a labor participation rate in the company's sample?
0.652 and 0.0454
It is known that 10% of the calculators shipped from a particular factory are defective. What is the probability that none in a random sample of four calculators is defective?
0.6561
Alex is in a hurry to get to work and is rushing to catch the bus. She knows that the bus arrives every six minutes during rush hour, but does not know the exact times the bus is due. She realizes that form the time she arrives at the stop, the amount of time that she will have to wait follows a uniform distribution with a lower bound of 0 minutes and an upper bound of six minutes. What is the probability that she will have to wait more than 2 minutes?
0.667
A random sample of size 36 is taken from a population with mean µ = 17 and standard deviation σ = 6. Use an appropriate normal transformation to calculate the probability that the sample mean is between 15 and 18.
0.8185
The number of homes sold by a realtor during a month has the following probability distribution: Number Sold Probability 0 0.30 1 0.20 2 0.50 The standard deviation of the number of homes sold by the realtor during a month is the closest to _________________.
0.87
A random sample of size 36 is taken from a population with mean µ = 23 and standard deviation σ = 6. Use an appropriate normal transformation to calculate the probability that the sample mean is between 21 and 25.
0.9544
The time for a professor to grade a student's homework in statistics is normally distributed with a mean of 13.1 minutes and a standard deviation of 2.0 minutes. What is the probability that randomly selected homework will require less than 17 minutes to grade?
0.9744
According to the Bureau of Labor Statistics it takes an average of 22 weeks for someone over 55 to find a new job. Assume that the probability distribution is normal and that the standard deviation is two weeks. What is the probability that eight workers over the age of 55 take an average of more than 20 weeks to find a job?
0.9977
According to geologists, the San Francisco Bay Area experiences five earthquakes with a magnitude of 6.5 or greater every 100 years. What is the standard deviation of the number of earthquakes with a magnitude of 6.5 or greater striking the San Francisco Bay Area in the next 40 years?
1.414
A nursery sells trees of different types and heights. These trees average 60 inches in height with a standard deviation of 16 inches. Suppose that 75 pine trees are sold for planting at City Hall. What is the standard deviation for the sample mean?
1.8475
What is Zα/2 for a 95% confidence interval of the population mean?
1.96
Consider the following probability distribution. xi P(X = xi) 0 0.1 1 0.2 2 0.4 3 0.3 The expected value and standard deviation are _____ and ________, respectively.
1.9; 0.943
If an exponential distribution has the rate parameter λ = 5, what is its expected value?
1/5
A random sample of size 36 is taken from a population with mean µ = 17 and standard deviation σ = 6. What are the expected value and the standard deviation for the sampling distribution of the sample mean?
17 and 1 respectively
A packaging company strives to maintain a constant temperature for its packages that require a specific temperature range. It is believed that the temperature of packages follows a normal distribution with a mean of 3 degrees Celsius and a standard deviation of 0.5 degree Celsius. Inspectors take weekly samples for five weeks of eight randomly selected boxes and report their temperatures. The five weekly sample means are shown in the table below. Week 1: 3.45 Week 2: 3.12 Week 3: 2.88 Week 4: 5.10 Week 5: 5.58 How many points are outside of the control limits?
2
A packaging company strives to maintain a constant temperature for its packages that require a specific temperature range. It is believed that the temperature of packages follows a normal distribution with a mean of 5 degrees Celsius and a standard deviation of 0.3 degree Celsius. Inspectors take weekly samples for five weeks of eight randomly selected boxes and report their temperatures. The five weekly sample means are shown in the table below. Week 1: 4.97 Week 2: 5.16 Week 3: 5.12 Week 4: 5.35 Week 5: 5.50 How many points are outside the control limits?
2
Consider the following probability distribution. xi P(X = xi) 0 0.1 1 0.1 2 0.1 3 0.7 The expected value and standard deviation are ________ and ________ respectively
2.4; 1.020
The GPA of accounting students in a university is known to be normally distributed. A random sample of 20 accounting students results in a mean of 2.92 and a standard deviation of 0.16. Construct the 95% confidence interval for the mean GPA of all accounting students at this university.
2.92±2.093(0.16/√20)
A medical devices company wants to know the number of hours its MRI machines are used per day. A previous study found a standard deviation of four hours. How many MRI machines must the company find data for in order to have a margin of error of at most 0.60 hour when calculating a 98% confidence interval?
242
An employee of the Bureau of Transportation Statistics has been given the task of estimating the proportion of on-time arrivals of a budget airline. A prior study has estimated this on-time arrival rate as 78.5%. What is the minimum number of arrivals this employee must include in the sample to ensure that the margin of error for a 95% confidence interval is no more than 0.05?
260
Chauncey Billups, a current shooting guard for the Los Angeles Clippers, has a career free-throw percentage of 89.4%. Suppose he shoots six free throws in tonight's game. What is the expected number of free throws that Billups will make?
5.364
Sarah's portfolio has an expected annual return at 8%, with an annual standard deviation at 12%. If her investment returns are normally distributed, then in any given year Sarah has approximately ______.
50% chance that the actual return will be greater than 8%
The time of a call to a technical support line is uniformly distributed between 2 and 10 minutes. What are the mean and variance of this distribution?
6 minutes and 5.333(minutes)^2
Heidi's portfolio has an expected annual return at 10%, with an annual standard deviation at 12%. If her investment returns are normally distributed, then in any given year Heidi has approximately ________.
68% chance that the actual return will fall within -2% and 22%
A marketing firm wants to estimate how much root beer the average teenager drinks per year. A previous study found a standard deviation of 1.12 liters. How many teenagers must the firm interview in order to have a margin of error of at most 0.1 liter when constructing a 99% confidence interval?
833
A marketing firm wants to estimate how much root beer the average teenager drinks per year. A previous study found a standard deviation of 1.19 liters. How many teenagers must the firm interview in order to have a margin of error of at most 0.1 liter when constructing a 99% confidence interval?
940
A consumer who is risk averse is best characterized as __________________________________________.
A consumer who demands a positive expected gain as a compensation for taking risk.
Which of the following statements is correct?
A continuous random variable has a probability density function, and a discrete random variable has a probability mass function.
Super Bowl XLVI was played between the New York Giants and the New England Patriots in Indianapolis. Due to a decade-long rivalry between the Patriots and the city's own team, the Colts, most Indianapolis residents were rooting heartily for the Giants. Suppose that 90% of Indianapolis residents wanted the Giants to beat the Patriots. What is the probability that from a sample of 40 Indianapolis residents, fewer than 95% were rooting for the Giants in Super Bowl XLIV?
Cannot be determined based on the given information
What is the relationship between the expected value of the sample mean and the population mean?
E (X¯) = μ .
For a given sample size and population standard deviation, which of the following is true regarding the confidence interval of the population mean?
If the confidence level gets larger, the confidence interval gets wider.
A continuous random variable has the uniform distribution on the interval [a, b] if its probability density function f(x) ______.
Is constant for all x values between a and b, and 0 otherwise.
Which of the following statements is the most accurate about a binomial random variable?
It counts the number of successes in a given number of identical trails
Which of the following is not a characteristic of the probability mass function of a discrete random variable X?
It is also called the probability density function of X, denoted by f(x).
How does the variance of the sample mean compare to the variance of the population?
It is smaller and therefore suggests that averages have less variation than individual observations
John would like to conduct a survey in his neighborhood to get homeowners' opinion on Delmarva proposal to switch to natural gas. Which of the following is an example of a stratified sample?
John randomly chooses three streets and selects every third house on those streets
The finite population correction factor is always ______.
Less than one, and therefore decreases the standard deviations of X (X with line over it) and P (P with line over it) computed under the assumption of infinite population
Which of the following is the necessary condition for creating confidence intervals for the population mean?
Normality of the estimator
What is the most typical form of a calculated confidence interval?
Point estimate +- Margin or error
The cumulative distribution function F(x) of a continuous random variable X with the probability density function f(x) represents
The area under f(x) over all values that are smaller than or equal to x.
When examining the possible outcome of an election, what type of confidence interval is most suitable for estimating the current support for a candidate?
The confidence interval for the population proportion
What can be said about the expected value and standard deviation of an exponential distribution?
The expected value is equal to the standard deviation
Which of the following does not represent a continuous random variable?
The number of customer arrivals to a bank between 9 am and 10 am.
The ages of MBA students at a university are normally distributed with a known population variance of 10.24. Suppose you are asked to construct a 95% confidence interval for the population mean age if the mean of a sample of 36 students is 26.5 years. If a 99% confidence interval is constructed instead of a 95% confidence interval for the population mean, then _______________________________________________.
The resulting margin or error will increase and the risk of reporting an incorrect interval will decrease
Bias can occur in sampling. Bias refers to ______.
The tendency of a sample statistic to systematically overestimate or underestimate a population parameter.
Which of the following is true about the hypergeometric distribution?
The trials are not independent and the probability of success may change for trail to trail
What conditions are required by the central limit theorem before a confidence interval of the population mean may be created?
The underlying population need not to be normally distributed if the sample size is 30 or more
Find the z value such that P(Z ≤ z) = 0.5398.
Z = 0.10
Which of the following is the correct formula for the margin of error in the interval estimation of p?
Zα/2√p(1−p)/n (make sure there is a line over the P's!!)
In an examination of purchasing patterns of shoppers, a sample of 16 shoppers revealed that they spent, on average, $54 per hour of shopping. Based on previous years, the population standard deviation is thought to be $21 per hour of shopping. Assuming that the amount spent per hour of shopping is normally distributed, find a 90% confidence interval for the mean amount.
[$45.36, $62.64]
A machine that is programmed to package 1.20 pounds of cereal is being tested for its accuracy in a sample of 36 cereal boxes, the sample mean filling weight is calculated as 1.22 pounds. The population standard deviation is known to be 0.06 pounds. Find the 95% confidence interval for the population mean filling weight.
[1.20, 1.24]
We draw a random sample of size 25 from a normal population with variance 1.9. If the sample mean is 16.5, what is a 95% confidence interval for the population mean?
[15.9600, 17.0400]
At an academically challenging high school, the average GPA of a high school senior is known to be normally distributed with a variance of 0.25. A sample of 20 seniors is taken and their average GPA is found to be 2.71. Develop a 90% confidence interval for the population mean GPA.
[2.5261, 2.8939]
We draw a random sample of size 36 from a population with standard deviation 3.5. If the sample mean is 27, what is a 95% confidence interval for the population mean?
[25.8587, 28.1433]
Which of the following is not a characteristic of a probability density function f(x)?
f(x) is always symmetric around the mean
Find the minimum sample size when we want to construct a 90% confidence interval on the population proportion for the support of candidate A in the following mayoral election. Candidate A is facing two opposing candidates. In a preselected poll of 100 residents, 22 supported her. The desired margin of error is 0.08.
n = 73
Under what condition is the finite population correction factor used for computing the standard error of X¯ and P¯ ?
n ≥ 0.05N
The confidence intervals for the population proportion are generally based on ___________.
the Z distribution
A 90% confidence interval is constructed for the population mean. If a 95% confidence interval had been constructed instead (everything else remaining the same), the width of the interval would have been _________and the probability of making an error would have been __________________.
wider; smaller
For quantitative data, the most appropriate control chart to monitor central tendency in a production process is a(n)
x (with line over it) chart