According to a recent poll, 26% 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. Assume the standard deviation from the recent studies is accurate and known. According to recent studies, cholesterol levels in healthy adults from the area average about 207 mg/dL, with a standard deviation of about 25 mg/dL, and are roughly Normally distributed. If the cholesterol levels of a sample of 42 healthy adults from the region is taken, answer parts (a) through (d). (a) What is the probability that the mean cholesterol level of the sample will be no more than 207? P(y overbarless than or equals207)equals nothing (Round to three decimal places as needed.)

0.5 = 50% probability that the mean cholesterol level of the sample will be no more than 207

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

What is the probability that the mean cholesterol level of the sample will be no more than 207?

This is the pvalue of Z when X = 207. So

By the Central Limit Theorem

has a pvalue of 0.5

0.5 = 50% probability that the mean cholesterol level of the sample will be no more than 207

450

step-by-step explanation:

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step-by-step explanation: