## Exercises for Finite Mathematics Applied to the Real World This Topic: Sampling Statisitics

1. According to coach Simon, the average height of male soccer players in the US is normally distributed with mean 1.79 m with a standard deviation of 0.04 m.

(a) In a randomly selected soccer team of 11 players, what is the probability that the average height of the players is less than 1.77 m?

(b) In view of the small sample size, must you make any additional assumptions to justify the answer? Explain.

2 A random sample of 49 teenagers was surveyed, and the average number of movies that they had rented in the past week was 1.9, with a sample standard deviation of 0.4. Construct a 95% confidence interval for the average number of movies rented by teenagers in a week.

 [, ] (lowest number first)

3. Having been fired from Sonic Video, you are trying to estimate how many resumes to send out. Your employment agent tells you that the average number of resumes that statistical consultants send out is 50. You don't believe it is that many, and you hypothesize that the average is less than 50. To "prove" it, you poll 100 of your colleagues and discover that they averaged only 47 resumes, with a standard deviation of 12 resumes. You then test your hypothesis at the 99% significance level. Are you justified in rejecting the agent's claim? (Justify with detailed calculations.)

Last Updated:April, 1999