Question

4) The National Health and Nutrition Examination survey estimated dietary intake of ten key
nutrients. One of those nutrients was calcium (mg). They found in all adults 60 years or older a
mean calcium intake of 721 mg with a standard deviation 454 mg. Assume that these values are
for the population mean and standard deviation for the US population. Also, assume that the
calcium intake measurements of this random variable have a population distribution shape that
is skewed to the right.
Suppose a random sample of 100 adults older than 60 years is to be taken and the sample mean
computed. Consider sampling distribution of the sample mean:
a. What is the mean of the sampling distribution of x ?
b. What is the shape of the sampling distribution of x ? Why did you make this conclusion?

Answer 1

=721

=454

n=100

#What is the mean of the sampling distribution of x.

Ans: = mean of the sampling distribution

  ==721

#mean of the sampling distribution=721

#. What is the shape of the sampling distribution of x ? Why did you make this conclusion?

Ans: shape of the sampling distribution of is normal .

Since it is lage sample, n > 30, the population need not be normal. Even for skewed population distributioin, the sampling dstribution of sample mean is normal by Central Limit Theorem

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