Oven thermostats were tested by setting them to 350◦F and measuring the actual temperature of the oven. In a sample of 67 thermostats, the average temperature was 348.2◦F and the standard deviation was 5.1◦F.

a. Find a 90% confidence interval for the mean oven temperature.

b. Find a 95% confidence interval for the mean oven temperature.

c. What is the confidence level of the interval (347.5, 348.9)?

d. How many thermostats must be sampled so that a 90% confidence interval specifies the mean to within ± 0.8◦F?

e. How many thermostats must be sampled so that a 95% confidence interval specifies the mean to within ± 0.8◦F?