Question 1034373: The National Health and Nutrition Examination Survey of 1976-80 found that the mean serum cholesterol level for U.S. males aged 20-74 years was 211. The standard deviation was approximately 90. Consider the sampling distribution of the sample mean based on samples of size 100 drawn from this population of males.
a. What are the mean and standard deviation of the sampling distribution?
b. Is it necessary for the original distribution to be normal? Explain.
c. Suppose a random sample of 100 is taken, what is the probability that the mean serum cholesterol level will be between 198 and 220?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! he National Health and Nutrition Examination Survey of 1976-80 found that the mean serum cholesterol level for U.S. males aged 20-74 years was 211. The standard deviation was approximately 90. Consider the sampling distribution of the sample mean based on samples of size 100 drawn from this population of males.
a. What are the mean and standard deviation of the sampling distribution?
mean of sample means = 211 ; std of sample means = 90/sqrt(100) = 9
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b. Is it necessary for the original distribution to be normal? Explain.
Not according to the Central Limit Theorem
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c. Suppose a random sample of 100 is taken, what is the probability that the mean serum cholesterol level will be between 198 and 220?
z(198) = (198-211)/9 = -1.44
z(220) = (220-211)/9 = 1
P(198 <= x-bar <= 220) = P(-1.44<= z <=1) = normalcdf(-1.44,1) = 0.7664
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Cheers,
Stan H
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