Question

Heights for group of people are normally distributed with mean = 63 inches and standard deviation = 4.0 inches. Find the proportion, P, of people in the group whose heights fall into the following ranges. (Round your answers to four decimal places.)

(a) Between 60 inches and 63 inches.

(b) Between 57 inches and 69 inches.

(c) Less than 69 inches.

(d) Greater than 57 inches.

(e) Either less than 57 inches or greater than 69 inches.

Answer 1

Mean = = 63

Standard deviation = = 4

a) We have to find P( 60 < X < 63)

For finding this probability we have to find z score.

That is we have to find P( - 0.75 < Z < 0)

P( - 0.75 < Z < 0) = P(Z < 0) - P(Z < - 0.75) = 0.5 - 0.2266 = 0.2734

b)

We have to find P( 57 < X < 69)

For finding this probability we have to find z score.

That is we have to find P( - 1.5 < Z < 1.5)

P( -1.5 < Z < 1.5) = P(Z < 1.5) - P(Z < - 1.5) = 0.9332 - 0.0668 = 0.8664

c) We have to find P(X < 69)

For finding this probability we have to find z score.

That is we have to find P(Z < 1.5)

P(Z < 1.5) = 0.9332

d) We have to find P(X > 57)

For finding this probability we have to find z score.

That is we have to find P(X > - 1.5)

P(X > - 1.5) = 1 - P(Z < - 1.5) = 1 - 0.0668 = 0.9332