PART A

Suppose you work as the qualoty control officer of a factory producing vaccum cleaners. You want to estimate the duration of trouble-free operation of a new vaccum cleaner. The duration of trouble-free operation is normally distributed with a standard deviation of 300 hours. You select a random sample of 25 vacuum cleaners and test them until they show the first signs of performance problems. The mean trouble-free duration for this sample is 2650 hours.

a. Construct a 90% confidence interval to estimate the mean durtion of trouble-free operation of this new vacuum cleaner.

b. Write a short summary/interpretation of your findings in part a.

PART B

An airline claims that  75%  of all its flights to Vancouver arrive on time. In a random sample of 60 recent arrivals,  40 were on time. You may assume that the normal distribution applies.

Verify that sampling distribution of porportion is normal.

Construct an 95% confidence interval for the proportion of flights arriving on  time.

Write a short interpretation of your findings in the last part.

Are your findings consistent with the airline claim? Explain.