Posted by **Jason L** on Monday, February 26, 2007 at 3:41pm.

It is known that the amount of time needed to change the oil in a car is normally distributed with a standard deviation of 5 minutes. A random sample of 100 oil changes yielded a sample mean of 22 minutes. Compute the 99% confidence interval estimate of the mean of the population.

Also determine the necessary sample size if you wish to be 99% confident and can tolerate an error of 1 minute.

Formula:

CI99 = mean + or - 2.575(sd divided by √n)

...where + or - 2.575 represents the 99% confidence interval using a z-table, sd = standard deviation, √ = square root, and n = sample size.

With your data:

CI99 = 22 + or - 2.575(5/√100)

Finish the calculation for your confidence interval estimate.

Formula for the second part:

n = [(z-value * sd)/E]^2

...where n = sample size, z-value will be 2.575 using a z-table to represent the 99% confidence interval, sd = 5, E = 1, ^2 means squared, and * means to multiply.

Plug the values into the formula and finish the calculation. Round your answer to the next highest whole number.

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