Chapter review

1)    The average age of doctors in a certain hospital is 48.0 years old. Suppose the distribution of ages is normal and has a standard deviation of 6.0 years. If 9 doctors are chosen at random for a committee, find the probability that the average age of those doctors is less than 48.8 years.
2) The length of country and western songs is normally distributed and has a mean of 170 seconds and a standard deviation of 40 seconds. Find the probability that a random selection of 16 songs will have mean length of more than 158.30 seconds.
3) The National Association of Realtors estimates that 23% of all homes purchased in 2004 were considered investment properties. If a sample of 900 homes sold in 2004 is obtained, what is the probability that fewer than 200 homes are going to be used as investment property?
4) A union official wanted to estimate the mean hourly wage of its members. A random
sample of 100 members gave a mean of $18.30 and standard deviation of $3.25 per hour. Find a 95% confidence interval for .
5) Construct a 99% confidence interval for the population mean, . Assume the population has a normal distribution. A sample of 20 part-time workers had mean annual earnings of $3120 with a standard deviation of $677.
6) A sample of 35 different payroll departments found that employees worked an average of 240.6 days a year, and the standard deviation is 18.8 days, find the 90% confidence interval for the average number of days worked by all employees who are paid through payroll departments.
7) A study of nickels showed that the standard deviation of the weight of nickels is 250
milligrams. A coin counter manufacturer wishes to find the 98% confidence interval for the average weight of a nickel. How many nickels does he need to weigh to obtain an average accurate to within 15 milligrams?
8) A sample of 400 racing cars showed that 80 of them cost over $700,000. What is the 99% confidence interval for the true proportion of racing cars that cost over $700,000?
9) A recent poll of 700 people who work indoors found that 278 smoke. If the researchers
want to be 98% confident of their results on proportion to within 3.5 percentage points, how large a sample is necessary?
10) For a random sample of 23 European countries, the variance on life expectancy was 7.3 years. What is the 95% confidence interval for the variance of life expectancy in all of
Europe?
11) If the confidence interval for p is (0.34, 0.42), find the sample proportion p and margin
of error E.
12) A recent study claimed that more than 10% of junior high students are overweight. In a sample of 160 students, 18 were found to be overweight. At = 0.05, test the claim.
13) A local retailer claims that the mean waiting time is less than 9 minutes. A random
sample of 20 waiting times has a mean of 7.4 minutes with a standard deviation of 2.1
minutes. At = 0.01, test the retailers claim. Assume the distribution is normally distributed.
14) A local group claims that the police on average issue more than 58 parking tickets a day in their area. To prove their point, they randomly select two weeks. Their research yields the number of tickets issued for each day. The data are listed below. At = 0.01, test the groups claim.
70 48 41 68 69 55 70 57 60 83 32 60 72 58
15) A shipping firm suspects that the variance for a certain brand of tire used by its trucks is greater than 1,000,000. To check the claim, the firm puts 101 of these tires on its trucks and gets a standard deviation of 1200 miles. At = 0.05, test the shipping firms claim.
16) In 2010, the mean expenditure for auto insurance in a certain state was $806. An
insurance salesperson in this state believes that the mean expenditure for auto insurance is less today. She obtains a simple random sample of 32 auto insurance policies and determines the mean expenditure to be $781 with a standard deviation of $39.13. Is there enough evidence to support the claim that the mean expenditure for auto insurance is less than the 2010 amount at the = 0.05 level of significance?

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