# Normal distribution and z-scores

1. For each of the following z-scores, sketch a normal distribution and draw a vertical line at the location of the z-score. Then, determine whether the tail is to the right or the left of the line and find the proportion in the tail.

a. z = 2.00

b. z = 0.50

c. z = -1.00

d. z = -0.75

2. The distribution of scores on the SAT is approximately normal with μ = 100 and σ = 100.

a. What proportion of the population have SAT scores above 650?

b. What proportion of the population have SAT scores below 540?

c. What is the minimum SAT score needed to be in the highest 20%

of the population?

d. What SAT score separates the top 60% from the rest of the

distribution?