Question

# According to a recent poll, 28% of adults in a certain area have high levels of...

According to a recent poll, 28% of adults in a certain area have high levels of cholesterol. They report that such elevated levels "could be financially devastating to the regions healthcare system" and are a major concern to health insurance providers. According to recent studies, cholesterol levels in healthy adults from the area average about 205 mg/dL, with a standard deviation of about 35mg/dL, and are roughly Normally distributed. Assume that the standard deviation of the recent studies is accurate enough to be used as the population standard deviation. If The cholesterol levels of a sample of 48 healthy adults from the region is taken, 207 mg/dL is the mean and 4.74 mg/dL is the standard deviation of the sampling distribution.

If the cholesterol levels of a sample of 48 healthy adults from the region is taken, the sampling distribution has the mean
μ(¯y)
of ___________, and the standard deviation SD(¯y) of _______________.

From the given information,

Sample mean=207

Sample standard deviation (s)=4.74

Sample size (n)=48

Now, Using central limit theorem,

μ(¯y)=Sample mean=207

And

standard deviation SD(¯y)=s/squareroot (n)

standard deviation SD(¯y)=4.74/squareroot (48)

Hence,

standard deviation SD(¯y)=0.6842

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