1. Using the standard normal distribution, find each probability.
a. P (z > 1.66)
b. P (z <-2.03)
c. P (z >-1.19)
d. P (z < 1.93)
e. P (z >-1.77)
2. For the first 7 months of the year, the average precipitation in Toledo, Ohio, is 19.32 inches. If the average precipitation is normally distributed with a standard deviation of 2.44, find these probabilities.
a. A randomly selected year will have precipitation greater than 18 inches for the first 7 years.
b. Five randomly selected years will have an average precipitation greater than 18 inches for the first 7 months.
3. For a certain urban area, in a random sample of 5 months, an average of 28 mail carriers were bitten by dogs each month. The standard deviation of the sample was 3. Find the 90% confidence interval of the true mean number of mail carriers who are bitten by dogs each month. Assume the variable is normally distributed.
4. A US Travel Data Center survey reported that Americans stayed an average of 7.5 nights when they went on vacation. The sample size was 1500. Find a point estimate of the population mean. Find the 95% confidence interval of the true mean. Assume the population standard deviation was 0.8.
5. Based on information from the U.S. Census Bureau, the mean travel time to work in minutes for all workers 16 years old and older was 25.3 minutes. A large company with offices in several states randomly sampled 100 of its workers to ascertain their commuting times. The sample mean was 23.9 minutes, and the population standard deviation is 6.39 minutes. At the 0.01 level of significance, can it be concluded that the mean commuting time is less for this particular company?
6. An advertisement claims that Fasto Stomach Calm will provide relief from indigestion in less than 10 minutes. For a test of the claim, 35 randomly selected individuals were given the product; the average time until relief was 9.25 minutes. From past studies, the standard deviation of the population is known to be 2 minutes. Can you conclude that the claim is justified? Find the P-value and let a = 0.05.
7. The average yearly earnings of male college graduates (with at least a bachelor's degree) are $58,500 for men aged 25 to 34. The average yearly earnings of female college graduates with the same qualifications are $49,339. Based on the results below, can it be concluded that there is a difference in mean earnings between male and female college graduates? Use the 0.01 level of significance.
8. The data show the amounts (in thousands of dollars) of the contracts for soft drinks in randomly selected local school districts. At a = 0.10, can it be concluded that there is a difference in the averages? Use the P-value method. Give a reason why the results would be of concern to a cafeteria manager.