Question

The heights of North American women are normally distributed with a mean of 64 inches and a standard deviation of 2 inches.

(a) What is the probability that a randomly selected woman is taller than 66 inches?

(b) A random sample of 40 women is selected. What is the probability that the sample mean height is greater than 66 inches?

Answer 1

Solution :

(a)

P(x > 66) = 1 - P(x < 66)

= 1 - P[(x - ) / < (66 - 64) / 2)

= 1 - P(z < 1)

= 1 - 0.8413

= 0.1587

Probability = 0.1587

(b)

= / n = 2 / 40 = 0.3162

P( > 66) = 1 - P( < )66

= 1 - P[( - ) / < (66 - 64) / 0.3162]

= 1 - P(z < 6.33)

= 1 - 1

= 0

Probability = 0