Question

Weights (X) of men in a certain age group have a normal distribution with mean μ = 160 pounds and standard deviation σ = 24 pounds. Find each of the following probabilities. (Round all answers to four decimal places.)

(a) P(X ≤ 190) = probability the weight of a randomly selected man is less than or equal to 190 pounds.

(b) P(X ≤ 148) = probability the weight of a randomly selected man is less than or equal to 148 pounds.

(c) P(X > 148) = probability the weight of a randomly selected man is more than 148 pounds.

Answer 1

Solution :

Given that ,

mean = = 160

standard deviation = = 24

a)

P(x 190) = P((x - ) / (190 - 160) / 24)

= P(z 1.25)

= 0.8944 Using standard normal table,

Probability = 0.8944

b)

P(x 148) = P((x - ) / (148- 160) / 24)

= P(z -0.5)

= 0.3085 Using standard normal table,

Probability = 0.3085

c)

P(x > 148) = 1 - P(x < 148)

= 1 - P((x - ) / < (148 - 160) / 24)

= 1 - P(z < -0.5)

= 1 - 0.3085 Using standard normal table.

= 0.6915

Probability = 0.6915