Question

Heights for group of people are normally distributed with mean = 60 inches and standard deviation = 2.5 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 59 inches and 60 inches. P =___ (b) Between 54 inches and 66 inches. P =___ (c) Less than 66 inches. P =____ (d) Greater than 54 inches. P =_____ (e) Either less than 54 inches or greater than 66 inches. P =____

Answer 1

Given,

= 60

= 2.5

a) between 59 inches and 60 inches.

We know that z = (x-​​​​​​) /

p(59 < x < 60) =p (59-60/2.5 < z < 60-60/2.5)

= p( -0.4 < z < 0)

= 0.1554

p(59 < x < 60) = 0.1554

b) p(54 < x< 66)

p(54 < x < 66) = p(54-60/2.5 < z < 66-60/2.5)

= p(-2.40 < z < 2.40)

= p( z < 2.40) + p(z < 2.40)

= 0.4918 + 0.4918

p(54 < x < 66) = 0.9836

Therefore between 54 inches and 66 inches is 0.9836.

3) less than 66 inches

p( x < 66) = 0.5 + p(0 < z < 66-60/2.5)

= 0.5 + p(0 < z < 2.40)

= 0.5 + 0.4918

p(x < 66) = 0.9918

d) greater than 54 inches

​​​​​​p(x > 54) = 0.5 + p(0 < z < 54-60/2.5)

= 0.5 + p(0 < z < -2.40)

= 0.5 + 0.4918

p(x > 54) = 0.9918