We are given that the average height for women in America is 64 inches tall with a standard deviation of 2.3 inches. Suppose we take a random sample of 31 women from America. Find the probability that the average height of those 31 women falls below 63 inches.
Solution:
Given: the average height for women in America is 64 inches tall with a standard deviation of 2.3 inches.
Sample Size = n = 31
Since sample size = n = 31 > 30 is large, thus using Central limit theorem, sampling distribution of sample mean follows an approximate Normal distribution with mean of sample means is:
and standard deviation of sample means is:
We have to find: the probability that the average height of those 31 women falls below 63 inches
Find z score:
Thus we get:
Look in z table for z = -2.4 and 0.02 and find area.
P( Z< -2.42 ) = 0.0078
thus
We are given that the average height for women in America is 64 inches tall with...
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