Question

In a survey of a group of​ men, the heights in the​ 20-29 age group were normally​ distributed, with a mean of 67.9 inches and a standard deviation of 4.0 inches. A study participant is randomly selected. a)Find the probability that a study participant has a height that is less than 67 inches. b) Find the probability that a study participant has a height that is between 67 and 72 inches. c)Find the probability that a study participant has a height that is more than 72 inches. d) Identify any unusual events.

Answer 1

z = (x - μ) / σ

a)Find the probability that a study participant has a height that is less than 67 inches.

z = (67-67.9)/4 = -0.225

P(Z < -0.225) = 0.4110

b) Find the probability that a study participant has a height that is between 67 and 72 inches

z = (67-67.9)/4 = -0.225

z = (72-67.9)/4 = 1.025

P(-0.225 < z < 1.025) = 0.4363

c)Find the probability that a study participant has a height that is more than 72 inches.

z = (72-67.9)/4 = 1.025

P(Z > 1.205) = 0.1527

d) Identify any unusual events.

Events are unusual if probablities are too small.Generally considered probability to be small when it is less than 0.05 or 5 %

There is no unusla events in the probability