1. Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper car loader is set to put 36 tons of coal in each car. The actual weights of coal loaded into each car are normally distributed with a mean µ. = 36 tons and a standard deviation σ = 0.8 tons.
(a) What is the probability that ONE car chosen at random will have -less than 35.5 tons of coal?
(b) What is the probability that 20 cars chosen at random will have a mean load weight x¯ less than 35.5 tons of coal?
(c) Suppose that the weight of coal in one car was less than 35.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? Suppose the weight of coal in 20 cars selected at random had an average x¯ less than 35.5 tons, Would that fact make you suspect that the loader had slipped out of adjustment? Why?
2. To be licensed as a practical nurse, one must make a score in the-top 30% on the licensing exam. The mean score of all students tiling the exam is 79 with a standard deviation of 9 points and the scores are given in whole number values. What is the least score a student can make and be considered in the top 30%?
3. Kate and Leopold are thinking about-buying the Rockwood Motel located on Interstate 70. Before they make up their mind, they want to estimate the average number of vehicles that go by the motel each day in the summer. Fortunately, the highway department has been counting vehicles on 1-70 near the motel. A random sample of 36 summer days shows a mean of 16,000 cats per day with a standard deviation of 2400 cars. Find a 75% confidence interval for the population mean number of cars per summer day going past the Rockwood Motel. Verbalize your result?
4. Andre is the head waiter at a famous gourmet restaurant in San Francisco. The Internal Revenue Service is doing an audit on his tax return this year· In particular, the IRS wants to know the average amount Andre gets for a tip. In an effort to satisfy the IRS, Andre took a random sample of 8 credit card receipts, each of which had his tip recorded. The results were as follows:
$10.00 $11.93 $15.70 $9.10
$12.75 $11.15 $14.50 $13.65
Find a 90% confidence interval for all tips received by Andre, using this sample.
5. Suppose, that 800 students were selected at random from student bodies at different colleges across the nation and given flu shots. All 800 students were then exposed to the flu, and 600 of them did not get the flu. Find a 99% confidence interval for the true proportion of all students whose flu shots would be successful in preventing them from getting the flu. Verbalize this revelation
6. A certain company makes light fixtures on an assembly line. An efficiency expert wants to determine the mean time if takes an employee to assemble the switch on one of these futures. A preliminary study used a random sample of 45 observations and found that the sample standard deviation was s = 78 seconds. How many more observations are necessary for the efficiency expert to be 95% sure that the point estimate x¯ will be in error from the true mean µ by at most 15 seconds?