Question 1. In a large metropolitan area, past records revealed that 30 percent of all the high school graduates go to college. Each student's choice to go to college is independent. From 20 graduates selected at random, what is the probability that exactly 8 will go to college?

Question 2. A statistics professor receives an average of five e-mail messages per day from students. Assume the number of messages approximates a Poisson distribution.
What is the probability that on a randomly selected day she will have two messages? 

Question 3. The time to fly between New York City and Chicago is normally distributed with a mean of 140 minutes and a standard deviation of 15 minutes. What is the z-score that corresponds to a random variable X outcome of 150 minutes?

Question 4. The time to fly between New York City and Chicago is normally distributed with a mean of 140 minutes and a standard deviation of 15 minutes. What is the probability that a flight is less than 135 minutes?

Question 5. The time to fly between New York City and Chicago is normally distributed with a mean of 140 minutes and a standard deviation of 15 minutes. What is the probability that a flight is more than 160 minutes?

Question 6. The time to fly between New York City and Chicago is normally distributed with a mean of 140 minutes and a standard deviation of 15 minutes. What is the probability that a flight takes between 140 and 160 minutes?

Question 7. The time to fly between New York City and Chicago is normally distributed with a mean of 140 minutes and a standard deviation of 15 minutes. What is the probability that a flight takes less than 140 minutes or greater than 160 minutes?

Question 8. After arriving at the university student medical clinic, the waiting times to receive service after checking-in follow an exponential distribution with a mean of 10 minutes. Calculate the probability a student waits more than 12 minutes. 

Question 9. The American Auto Association reports the mean price per gallon of regular gasoline is $3.10 with a population standard deviation of $0.20. Assume a random sample of 16 gasoline stations is selected and their mean cost for regular gasoline is computed.
What is the probability that the sample mean is between $2.98 and $3.12? 

Question 10. The American Auto Association reports the mean price per gallon of regular gasoline is $3.10 with a population standard deviation of $0.20. Assume a random sample of 16 gasoline stations is selected and their mean cost for regular gasoline is computed.
What is the probability that the sample mean is greater than $3.08?

Question 11. The American Auto Association reports the mean price per gallon of regular gasoline is $3.10 with a population standard deviation of $0.20. Assume a random sample of 16 gasoline stations is selected and their mean cost for regular gasoline is computed.
95% of the sample means fall within what two limits?

Question 12. LongLast Inc. produces car batteries. The mean life of these batteries is 60 months. The distribution of the battery life closely follows the normal probability distribution with a standard deviation of 8 months. As a part of its testing program, LongLast tests a sample of 25 batteries.
What percentage of the samples will have a mean useful life less than 56 months? 

Question 13. A population consists of the following four values: 8, 10, 12, and 16. From this population, there are 6 different samples of size 2. The means of the 6 samples of size 2 are: 9, 10, 12, 11, 13, and 14. Compute the mean of the distribution of the sample means and the population mean.
Compare the two values. What is true about the two values?

Question 14. A research firm conducted a survey to determine the mean amount people spend at a popular coffee shop during a week. They found the amounts spent per week followed a normal distribution with a population standard deviation of $4. A sample of 64 customers revealed that the mean is $25.
What is the 99.6% confidence interval estimate of µ? (Be sure to calculate the actual confidence interval end points / limits in real dollars).

Question 15. A local health care company wants to estimate the mean weekly elder day care cost. A sample of 10 facilities shows a sample mean of $250 per week with a SAMPLE standard deviation of $25.
What is the 95% confidence interval for the population mean? (Be sure to calculate the actual confidence interval end points / limits in real dollars).

Question 16. A population is estimated to have a standard deviation of 25. We want to estimate the population mean within 2, with a 95% level of confidence.
How large of a sample is required? 

Question 17. A silkscreen printing company purchases t-shirts. To ensure the quality of the shipment, 300 t-shirts are randomly selected. 15 are defective.
What is the 95% confidence interval for the proportion defective?