Finding probability using population mean and sample standard deviation

Question

Greenleaf Lawn Care finds that the population mean cost of leasing homes in the area is $1250. If 20 homes are randomly selected, the standard deviation in the sample is s = $963. What is the probability that the mean of home leasing in the area is less than $2,895? Assuming population is normally distributed.

Answer 1

First, a guess. To the left of about two standard deviations above the mean will be ~95%.

Next, find a normal variable t = [ χ - µ ] / (s / √n)

t = [2895 - 1250] / (963 / √20) = 7.64

Degrees of freedom df = n-1 = 19

Lastly, use a t-table to find the area under the curve (the probability) left of t=7.64 with df=19