Question

Heights US males closely follow a normal distribution with mean 70 inches and standard deviation 3.3 inches.

(a) What is the probability that a randomly chosen man is shorter than 65 inches?

(b) What is the probability that a randomly chosen man is between 65 and 70 inches?

(c) What is the chance that a randomly selected man is taller than six feet (72inches)?

Answer 1

a)

X ~ N ( µ = 70 , σ = 3.3 )
We convert this to standard normal as
P ( X < x ) = P ( Z < ( X - µ ) / σ )
P ( ( X < 65 ) = P ( Z < 65 - 70 ) / 3.3 )
= P ( Z < -1.52 )
P ( X < 65 ) = 0.0643 (From Z table)

b)

Given :- = 70 , = 3.3 )
We convet this to Standard Normal as
P(X < x) = P( Z < ( X - ) / )
P ( 65 < X < 70 ) = P ( Z < ( 70 - 70 ) / 3.3 ) - P ( Z < ( 65 - 70 ) / 3.3 )
= P ( Z < 0) - P ( Z < -1.52 )
= 0.5 - 0.0643 (From Z table)
= 0.4357

c)

X ~ N ( µ = 70 , σ = 3.3 )
We covert this to standard normal as
P ( X < x) = P ( (Z < X - µ ) / σ )
P ( X > 72 ) = P(Z > (72 - 70 ) / 3.3 )
= P ( Z > 0.61 )
= 1 - P ( Z < 0.61 )
= 1 - 0.7291 (From Z table)
= 0.2709