Question

Weights (X) of men in a certain age group have a normal distribution with mean μ = 190 pounds and standard deviation σ = 20 pounds. Find each of the following probabilities. (Round all answers to four decimal places.)

(a) P(X ≤ 220) = probability the weight of a randomly selected man is less than or equal to 220 pounds.


(b) P(X ≤ 165) = probability the weight of a randomly selected man is less than or equal to 165 pounds.


(c) P(X > 165) = probability the weight of a randomly selected man is more than 165 pounds.

Answer 1

Solution :

Given that ,

mean = = 190

standard deviation = = 20

a) P(x 220)

= P[(x - ) / (220 - 190) / 20]

= P(z 1.50)

Using z table,

= 0.9332

b) P(x 165)

= P[(x - ) / (165 - 190) / 20]

= P(z -1.25)

Using z table,

= 0.1056

c) P(x > 165 ) = 1 - p( x< 165)

=1- p P[(x - ) / < (165 - 190) / 20]

=1- P(z < -1.25)

Using z table,

= 1 - 0.1056

= 0.8944