Question

Suppose that a garage tells its customers that with the new synthetic oil that the average time people wait for an oil change is 5734.2 miles with a standard deviation of 1011.9 miles. What is the mileage of the top 10% of who wait to bring their in for an oil change?

Answer 1

The top 10% of customers wait to bring their car in for an oil change at approximately 7029.43 miles, based on the normal distribution, a mean of 5734.2 miles, a standard deviation of 1011.9 miles, and a z-score of 1.28.

Step-by-step explanation:

To find the mileage at which the top 10% of customers wait to bring their car in for an oil change, given a mean of 5734.2 miles and a standard deviation of 1011.9 miles, we need to use the concept of z-scores and the normal distribution. The z-score corresponding to the top 10% can be found using a z-table or a statistical calculator, which is approximately 1.28. The formula to calculate the specific mileage value (X) is:

X = μ + (z * σ)

Where μ is the mean, z is the z-score, and σ is the standard deviation. Plugging in the values, we get:

X = 5734.2 + (1.28 * 1011.9)

Calculating this, we find:

X = 5734.2 + 1295.23

X = 7029.43 miles

So, the mileage at which the top 10% of customers wait to bring their car in for an oil change is approximately 7029.43 miles.