Question

Assume that women's heights are normally distributed with a mean of 63.6 inches and standard deviation of 3 inches. If 36 woman are randomly selected, find the probability that they have a mean height between 63.6 and 64.6 inches.

Answer #1

Solution :

Given that,

mean = = 63.6

standard deviation = = 3

= / n = 3/ 36 = 0.5

= P[(63.6 - 63.6) /0.5 < ( - ) / < (64.6 - 63.6) / 0.5)]

= P(0 < Z < 2)

= P(Z < 2) - P(Z < 0)

= 0.9772 - 0.5

0.4772

Probability = 0.4772

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