Directions: Draw the normal curve and shade in the specific region. Show formulas used and the substitution. Assume that the salaries of the elementary school teachers in the United States with a mean...

Directions: Draw the normal curve and shade in the specific region. Show formulas used and the substitution.

Assume that the salaries of the elementary school teachers in the United States with a mean of 31,000 dollars and a standard of 3000 dollars.

a. If 100 teachers are randomly selected, find the probability that their mean salary is greater than 31,500 dollars.

b. If 120 teachers are selected, what is the probability that their mean salary is greater than 31,500? So as the sample size increases, what happens to the probability value.

c. If the 120 teachers are randomly selected what is the probability that their mean salary is between 31,200 to 31,500