The empirical rule states that for bell-shaped distributions, about 68% of the v

Question

The empirical rule states that for bell-shaped distributions, about 68% of the values fall within 1 standard Deviation of the mean. The heights of women at a large university are approximately bell-shaped, with a mean of 64 inches and standard of 2 inches. Use this information to answer the question. 1) what is the probability that of two randomly selected women, one is 66 inches or shorter and the other is 66 inches or taller? ( answer to four decimal places) The empirical rule states that for bell-shaped distributions, about 68% of the values fall within 1 standard Deviation of the mean. The heights of women at a large university are approximately bell-shaped, with a mean of 64 inches and standard of 2 inches. Use this information to answer the question. 1) what is the probability that of two randomly selected women, one is 66 inches or shorter and the other is 66 inches or taller? ( answer to four decimal places) 1) what is the probability that of two randomly selected women, one is 66 inches or shorter and the other is 66 inches or taller? ( answer to four decimal places)

Explanation / Answer

Using central limit theorem the sampling distribution of sample mean is also normal with mean same as population mean =64 inches and standard deviation =sigma/root over n=2/root over 2=1.41

Thus for X=66, z=(x-mu)/sigma=(66-64)/1.41=1.41

P(X>=66)=1-P(X<=66)=1-P(z<=1.41)=1-0.9207=0.0793

P(X<=66)=0.9207

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