The study in Example 5 found that 32.0% of all men in the United States ages 50 and older have arthritis. You randomly select 75 men in the United States who are at least 50 years old and ask them whether they have arthritis. What is the probability that exactly 15 will say yes?

a. Determine whether you can use a normal distribution to approximate the binomial variable.

b. Find the mean μ and the standard deviation σ for the normal distribution.

c. Apply a continuity correction to rewrite P(x = 15) and sketch a graph.

d. Find the corresponding z-scores.

e. Use the Standard Normal Table to find the area to the left of each z-score and calculate the probability.