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Answer:
The sampling distribution of x is N(118, 2.5).
Step-by-step explanation:
We have that:
The mean of the population is
The standard deviation of the population is .
(a) Choose an SRS of 100 men from this population. What is the sampling distribution of x? (Use the units of mg/dL.)
The mean of the sampling distribution is the same as the mean of the population.
The standard deviation of the sampling distribution is the standard deviation of the population divided by the square root of the sample size. So
This means that the sampling distribution of x is N(118, 2.5).
Expanding the terms,
Collecting like terms,
Evaluating the terms,
Divide both sides by -15,