Assume that cholesterol levels of men in the U.S. are normally distributed with a mean of 215 milligrams per deciliter and a standard deviation of 25 milligrams per deciliter.

What is the probability that a randomly selected man in the U.S. has a cholesterol level between 190 and 202.5 milligrams per deciliter?

Question

09-11-2023
Mathematics

High School

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Assume that cholesterol levels of men in the U.S. are normally distributed with a mean of 215 milligrams per deciliter and a standard deviation of 25 milligrams per deciliter.

What is the probability that a randomly selected man in the U.S. has a cholesterol level between 190 and 202.5 milligrams per deciliter?

Answer :

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Final answer:

The probability that a randomly selected man in the U.S. has a cholesterol level between 190 and 202.5 milligrams per deciliter is approximately 0.1498, or 14.98%.

Explanation:

To find the probability that the cholesterol level is between 190 and 202.5, we need to standardize the values using the z-score formula. The z-score is calculated by subtracting the mean from the value and dividing by the standard deviation. For 190, the z-score is (190 - 215) / 25 = -1, and for 202.5, the z-score is (202.5 - 215) / 25 = -0.5. We can then use a standard normal distribution table or calculator to find the probability associated with these z-scores.

Using the table, the probability of a z-score of -1 is 0.1587, and the probability of a z-score of -0.5 is 0.3085. Since we are looking for the probability between these two values, we subtract the lower probability from the higher probability: 0.3085 - 0.1587 = 0.1498. Therefore, the probability that a randomly selected man in the U.S. has a cholesterol level between 190 and 202.5 milligrams per deciliter is approximately 0.1498, or 14.98%.

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