Question

Suppose the population of all public universities shows the annual parking fee per student is $110, with a standard deviation of $18. if a random sample size of 49 is drawn from the population, the probability of drawing a sample with a sample mean between $100 and $115 is _______.

Answer 1

The probability would be 0.9738.

We first find the z-score for each end of this interval:

z = (x-μ)/(σ/√n) = (100-110)/(18/√49) = -10/(18/7) = -3.89

z = (x-μ)/(σ/√n) = (115-110)/(18/√49) = 5/(18/7) = 1.94

Using a z-table (http://www.z-table.com) we see that the probability that a score is less than the first z-score is 0.  The probability under the curve to the left of, less than, the second z-score is 0.9738.  Subtracting these we find the area between them:
0.9738 - 0 = 0.9738.