1). Movie theaters nation-wide are interested in determining the frequency that members of the public attend movies in theaters in the past 12 months. As a result the National Association of Theaters Owners commissions Info Inc. to take an opinion poll to determine this information. Info Inc. calls 1800 randomly chosen residential telephone numbers and asks to speak with an adult member of the household. The interviewer asks, “How many movies have you watched in a movie theater in the past 12 months. When the results are tabulated, Info Inc. reports that the average was 5 movies attended. Was this a probability (random) or non-probability (non random) sample? Carefully Explain. Do you think that the average number of movies attended is as high, or is it higher than the average of 5 reported in the sample? Carefully Explain.
2. A manufacturer is aware that the lifetime of batteries the firm produces is normally distributed. A random sample of 10 batteries shows a mean lifetime of 6 hours with a standard deviation of 1 hour. Construct a 99 percent confidence interval for the mean lifetime of all batteries produced by the same process.
Mean = 6
CI= 2.58 at 99%
6+- 2.58 (1/sqrt10)
6 +- 2.58(.316)
Confidence Interval = 6+- .81
3. Owens Orchards sells apples in a large bag by weight. A sample of five bags contained the following numbers of apples: 20, 18, 25, 15, 18.
a. Calculate the mean.
• 20+18+25+15+18/5 = 19.2
b. Calculate the variance.
• 20-19.2 = .8
So squared is … .64+1.44+33.64+17.64+1.44= 54.80
54.81/5-1 = 13.7
4. The miles-per-gallon (mpg) rating of cars is a normally distributed random variable with a mean of 25.9 and a standard deviation of 2.45. If an automobile manufacturer wants to build a car with an mpg rating that improves upon 99 percent of existing cars, what must the new car’s mpg rating be?
Mean = 25.9
5. There are 200 gas stations in a city; an economist takes a random sample of 50 of them. Their average gasoline price is $3.839, with a sample standard deviation is 23.10 cents per gallon. Determine a 90 percent confidence interval for the average price citywide, while assuming that the population distribution of gas prices is normal.
CI = 1.66 at 90%
3.839+- 1.66 (23.10/sqrt50)
Confidence Interval = +-5.37
6. A production process creates aircraft engines with an average life of 2,500 hours and a standard deviation of 400 hours. A simple random sample of 50 engines is taken and their life span is determined. Compute the probability of finding a sample mean that lies within 50 hours of the population mean
7. A manufacturer of strapping tape claims that the lengths of tape on the firm’s rolls have a mean of 90.10 feet and a standard deviation of 1.4. If you take a random sample of 49 units of the firm’s output what do you conclude about the truthfulness of the manufacturers claim if the sample mean is 89.5? Explain.
8. A pharmaceutical company deliberately infects 20 volunteers and then tests a new drug on them, finding a mean recovery time of 8 days, with a standard deviation of 2.5 days. Construct a 95 percent confidence interval for the mean recovery time of all potential users of this drug on the assumption that recovery times are normally distributed.
9. A company administers a test to all its employees. Test scores as well as finishing times are normally distributed random variables. If the average time required to finish the test equals 60 minutes, with a standard deviation of 12 minutes, when should the exam be terminated so that 95 percent of the workers have completed all parts of the test?
10. A would-be new telephone company is aware that the population of telephone-call durations in its potential market is normally distributed with a standard deviation of 4 minutes. In order to protect their revenues, the firm’s executives need to know the average duration of calls originating in the area. A sample of 50 calls yields a mean duration of 9.1 minutes. Construct a 95 percent confidence interval for the mean duration of all calls.
11. In a large city, an ambulance takes an average of 12 minutes to arrive after an emergency call; the standard deviation is 4 minutes. Compute the probability of finding a sample mean of between 13 and 14 minutes.
12. The manufacturer of batteries for aircraft emergency vehicles claims that lifetime of the 1500 batteries that have been manufactured is normally distributed with a mean of 30 months and a standard deviation of 3 months. An aircraft manufacturer checks out 50 batteries that they purchased and discovers a sample mean of 29 months. What is probability of finding a sample mean of 29 months or less?