Question

Please show your work

The heights, H, of the people in a certain town are normally distributed with mean 170 cm and standard deviation 20 cm.

(a) A person is selected at random. Find the probability that his height is less than 185 cm.

(b) Given that P (H > d) = 0.6808, find the value of d.

Answer 1

Solution:

We are given

µ = 170

σ = 20

Part a

We have to find P(X<185)

Z = (X - µ)/σ

Z = (185 - 170)/20

Z = 0.75

P(Z<0.75) = P(X<185) = 0.773373

(by using z-table)

Required probability = 0.773373

Part b

P(H>d) = 0.6808

P(H<d) = 1 – 0.6808 = 0.3192

Z = -0.46994

d = µ + Z*σ

d = 170 + (-0.46994)*20

d = 160.6012

Answer: d = 160.6012