The probability is approximately

Question

What is the probability that a random sample of n=35 oil changes results in a sample mean time less than 20 ​minutes? The probability is approximately

Answer 1

This question sounds like it is straight off of your homework except that you left off some important information. If this is all that you have, then you can't find a numerical answer to this problem. It sounds like you are looking to find the probability on a sampling distribution where you were given a population mean and a population standard deviation. If you have these, then you might want to refer back to the sections where you talked about what the sampling distribution would look like (the index at the back of your book can help with this.) Hopefully there will be some examples there that can help.

If the population mean (the mean of all oil change durations) was 30 min with a population standard deviation (the standard deviation for ALL oil changes, not just this sample) is 5 minutes, then you are trying to find

P(X ≤ 20)

where x is normally distributed with a mean of 30 and a standard deviation of 5/√(35)

I hope that you can do the rest. This should be similar to finding areas under the curve or probabilities when you were working with z-scores.

If you are not given the population standard deviation, but instead a sample standard deviation, then you will need to do something similar, but you will be using a t-distribution instead of z-distribution. The main difference being that you will use 5/√(35-1) for the standard deviation and that you will need to use df = 35-1 for your degrees of freedom. If you haven't talked about that yet, then you probably don't need it right now.