The mean value of land and buildings per acre for farms in Colorado is $1170. A random sample of 32 Colorado farms is selected. What is the probability that the mean value of land and buildings per acre for the sample is

(a) Less than $1200,

(b) More than $1275, and

(c) Between $1100 and 1250?

Assume σ = $200.

Find the indicated probabilities and interpret the results. If convenient, use technology to find the probabilities.