normal distribution with a mean of 71 inches and a standard deviation of 3 inches. Find the probability that a randomly selected man has a height between 69 inches and 73 inche

Question

Men’s heights are distributed as the normal distribution with a mean of 71 inches and a standard deviation of 3 inches. Find the probability that a randomly selected man has a height between 69 inches and 73 inches

Answer 1

Let x be height we want to find P(69 < x < 73)

Transform limits of above inequality to standard normal:

z = (x - mean)/SD

For x = 69, z = (69 - 71)/3 = -0.67

For x = 73, z = (73 - 71)/2 = 0.67

so P(69 < x < 73) = P(-0,.67 < z < 0.67) = P(z < 0.67) - P(z < 0.67)