Question

The heights of 18-year-old men are approximately normally distributed with mean 68 inches and standard deviation 3 inches. What is the probability that the height of an 18-year-old man selected at random is between 66 inches and 67 inches? 0.8807 0.4283 0.1193 0.3807 0.1333.

Answer 1

Let X be the random variable that denotes the height of an 18-year-old man.

Given, X is normally distributed with mean = 68 inches and standard deviation = 3 inches.

X Normal ( = 68, = 3)

P(66 < X < 67) = P((66 - 68) / 3 < Z < (67 - 68) / 3))

                        = P( -0.67 < Z < -0.33)

                        = P(Z < -0.33) - P(Z < -0.67)

                        = P(Z > 0.33) - P(Z > 0.67)    .............( P(Z < -a) = P(Z > a))

                        = (1 - P(Z < 0.33)) - (1 - P(Z < 0.67))

                        = P(Z < 0.67) - P(Z < 0.33)

                        = 0.74857 - 0.62930    .............(values from standard normal table)

                        = 0.11927

Therefore, the probability that the height of an 18 year-old man selected at random is between 66 inches and 67 inches is 0.1193