In an article titled “Airport screeners’ strains, sprains highest among workers,” Thomas Frank reported that the injury rate for airport screeners was 29%, far exceeding the 4.5% injury rate for the rest of the federal workforce. The 48,000 full- and part-time screeners were reported to have missed nearly a quarter-million days because of injuries in the recent fiscal year.

(Source: Thomas Frank, USA Today, http://usatoday30.

usatoday.com, Jan. 10, 2006.)

a. Calculate the average number of days airport screeners missed.

b. If one were to estimate the average number of days missed to within 1 hour in 2006 with a confidence level of 90%, determine the smallest sample size that would be required. Assume the standard deviation of the number of days missed is 1.5 days and that a work day consists of 8 hours.

c. How close could the estimate get if a sample of size 100 was used?