8 Students arrive at a local bar and restaurant according to

8. Students arrive at a local bar and restaurant according to an approximate Poisson process at a mean rate of 30 students per hour. A bouncer is at the door carding students as they enter.

a) What is the mean number of students arriving every minute?

b) What is the probability that the bouncer has to wait more than 3 minutes to card the next student? (1 pt.)

c) The bouncer has to make a quick “pit-stop.” What interval of time does the bouncer have to the nearest tenth of a minute to make that stop with a probability of .50 with the next student arriving?

9. Intravenous fluid bags are filled by an automated filling machine. Assume that the fill volumes of the bags are independent, normal random variables with a standard deviation of 0.08 fluid ounce.

(a) What is the standard deviation of the average fill volume of 20 bags?

(b) If the mean fill volume of the machine is 6.16 ounces, what is the probability that the average fill volume of 20 bags is below 5.95 ounces?

(c) What should the mean fill volume equal in order that the probability that the average of 20 bags is below 6 ounces is 0.001? Your answer to three decimal places.

10. Benzene is a toxic chemical used in the manufacturing of medicinal chemicals, dyes, artificial leather, and linoleum. A manufacturer claims that its exit water meets the federal regulation with a mean of less than 7980 ppm of benzene. To assess the benzene content of the exit water, 10 independent water samples were collected and found to have an average of 7906 ppm of benzene. Assume a known standard deviation of 80 ppm and use a significance level of 0.01.

(a) Test the manufacturer’s claim. Use the P-value approach.

(b) What is the -value if the true mean is 7920?

(c) What sample size would be necessary to detect a true mean of 7920 with a probability of at least 0.90?

(d) Find a 99% one-sided upper confidence bound on the true mean.

11. The sodium content of twenty 300-gram boxes of organic cornflakes was determined. The data (in milligrams): = 129.75, s = .876 and sample size = 20.

(a) Can you support a claim that mean sodium content of this brand of cornflakes differs from 130 milligrams? (Hint: ) Use = 0.05. Find the P-value.

(b) Compute the power of the test if the true mean sodium content is 130.5 milligrams.

(c) What sample size would be required to detect a true mean sodium content of 130.1 milligrams if you wanted the power of the test to be at least 0.75?

12. A random sample of 500 registered voters in Phoenix is asked whether they favor the use of oxygenated fuels year round to reduce air pollution. If more than 318 voters respond positively, we will conclude that at least 60% of the voters favor the use of these fuels.

(a) What is the probability of Type I error if exactly 60% of the voters favor the use of these fuels.

(b) What is the Type II or error if 65% of the polled voters favor this action?

(1 pt.)

(c) If the true proportion of voters favoring this action is 65% what sample size of voters is required to be polled to have a power of 90%? (1 pt.)

Solution