Question

The distribution of heights for adult men in a certain population is approximately normal with mean 70 inches and standard deviation 4 inches. Which of the following represents the middle 80 percent of the heights? 50 inches to 73.37 inches A 62 inches to 78 inches B 64.87 inches to 75.13 inches C 66 inches to 74 inches D 66.63 inches to 90 inches E Submit

Answer 1

Solution:-

Given that,

mean = = 70

standard deviation = = 4

Using standard normal table,

P( -z < Z < z) = 80%

= P(Z < z) - P(Z <-z ) = 0.80

= 2P(Z < z) - 1 = 0.80

= 2P(Z < z) = 1 + 0.80

= P(Z < z) = 1.80 / 2

= P(Z < z) = 0.90

= P(Z < 1.282) = 0.90

= z  ± 1.282

Using z-score formula,

x = z * +

x = -1.282 * 4 + 70

x = 64.87 inches

Using z-score formula,

x = z * +

x = 1.282 * 4 + 70

x = 75.13 inches.

The middle 80% are from 64.87 inches to 75.13 inches