Statistics Example Problems

1. A university wants to estimate the average amount of money that students spend on books in a semester. It takes a random sample of 45 students and finds that the average amount of money spent was $282 with a standard deviation of $21. Find a 95% confidence interval estimate for the true mean amount of money spent on books in a semester.

2. A local public television station, which broadcasts educational programs, is soliciting contributions from its audience during pledge week. The master of ceremonies states that the average contribution of its members is $47. do you think that this average is the mean mode or median? Why?

3. A survey found that 30% of pet owners had their pets bathed professionally rather than doing it themselves. If 18 pet owners are randomly selected find the probability that exactly 5 people have their pets professionally bathed.

4. The Statistical Bulletin published by the Metropolitan life insurance company reported 2% of all Americans birth results in twins. If a random sample of 8000 births is taken, find the mean, variance and standard deviation of the number of births that would result in twins.

5. It was found that 60% of Americans victims of health care fraud are senior citizens. If 10 victims are randomly selected, find the probability that exactly 3 are senior citizens.

6. Find the mean, mode, median, variance and standard deviation of the following data:
35
45
30
35
40
25

7. A survey of 30 adults found that the mean age of a person's primary vehicle is 5.6 years. Assuming the standard deviation of the population is .8 years, find the 95% confidence interval of the population mean.

8. Find everything to the left of Z= 2.42

9. Find everything to the right of Z= -1.68

10. Find everything in between -1.68 and 2.42