3) One of the services that a body shop offers is full repainting of a car. The

Question

3) One of the services that a body shop offers is full repainting of a car. The shop is designing a new facility and they're trying to decide how many painting bays they should include by evaluating the mean time to paint a car. A sample of 5 cars were painted and the mean time to complete them was 3.9 hours. Historically, the standard deviation of the time to paint a car, o, is 0.4 hours. a) Calculate a 98% two-sided confidence interval for the mean time to paint a car, . b) The shop plans to operate each painting bay for 72 hours per week. Using the lower and upper limits on your interval from part (a), what is the range for the mean number of cars that can be painted in a single bay in a week? (i.e., determine the number of cars that could be painted if mean time were equal to your lower limit and if it were equal to your upper limit.)

Explanation / Answer

Anwer to the question is as follows:

a. Sample of 5 cars , sample mean is 3.9 hours, Standard dev = .4 hours

98% 2 sided interval has a t value of 3.747 at a df of n-1=5 = 4

So, a 98% 2 sided CI is given by : Sample mean+/- t*sigma/sqrt(n)

= 3.9 +/- 3.747*.4/sqrt(5) = 3.229 to 4.5703

b. So keeping total hours of 72 , we have this range at (72/15.754) to (72/22.293 )
or 22.3 to 15.8 cars per week. We will round off to the exact numbers since no. of cars can't exist in fractions. So, 15 to 22 is the right answer

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