## Related questions with answers

According to the Gallup Poll, $27\%$ of U.S. adults have high levels of cholesterol. Gallup reports that such elevated levels "could be financially devastating to the U.S. healthcare system" and are a major concern to health insurance providers. According to recent analyses, cholesterol levels in healthy U.S. adults average about $215 \mathrm{mg} / \mathrm{dL}$ with a standard deviation of about $30 \mathrm{mg} / \mathrm{dL}$ and are roughly Normally distributed. If the cholesterol levels of a sample of 42 healthy U.S. adults are taken, what is the probability that the mean cholesterol level of the sample:

a) Will be no more than 215?

Solutions

VerifiedIn this exercise, we are tasked to determine the probability that the mean cholesterol level of the 42 samples will be at most 215 mg/dL.

Let us define the random variable $Y$ as the BMI level of the randomly selected New Zealand adult aged $15$ and over. We know that the distribution of $Y$ is roughly normal with mean $\mu=26$ $kg/m^2$ and standard deviation $\sigma=3.5$ $kg/m^2$.

We were asked to compute for the probability that the mean $\bar{Y}$ of a sample of $n=42$ New Zealand adults will be no more than $26$ $kg/m^2$.

We can write this as $P(\bar{Y}\leq26)$.

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