The average number of police officers employed in a sample of cities that serve populations of 500,000 or more is 24.3. The sample has a standard deviation to 4.1. Based on this information and assuming the population is normally distributed answer the following questions. You MUST show your work to receive credit. You can type it in the box, upload a .pdf or picture, or use the equation editor.

a. What is the z-score that corresponds to having 15 officers employed in a department?

b. Interpret this z-score (1.5 points)

c. What percentage of departments employ less than 15 officers?

d. What proportion of departments employ between 20 and 23 officers?

e. What percentage of departments employ between 21 and 27 officers?