Question

The shape of the distribution of the time required to get an oil change at a 10 minute-oil- change facility is unknown. However, records indicate that the mean time for an oil change is 11.4 minutes, and the standard deviation for oil-changes is 3.2 minutes. A random sample of 40 oil change times is collected.

1. What conditions are met? Confirm independence of the sample with one condition, and confirm that the normal model is appropriate by referring to the sample size.

2. What is the model for the sampling distribution?

3. What is the probability that this sample will have a mean oil-change time of less than 10 minutes?

Answer 1

ANSWER:

Let X be the time required to get an oil change done on any given instant. We know that X has a mean minutes and standard deviation minutes

1. Calculate the probability that a random sample of oil changes results in a sample mean time of less than 10 minutes.

   

   Hence, the required probability is

2. Calculate the mean oil changes time would there be a 10% chance of being at or below.

   

   Hence, the required answer is