Question

Total cholesterol in children aged 10-15 is assumed to follow a normal distribution with a mean of 191 and a standard deviation of 22.4. A sample of 20 children is selected. What is the probability that the mean cholesterol level of the sample will be greater than 200?

Answer 1

The probability that the mean cholesterol level of the sample will be greater than 200 is approximately 0.2524.

Step-by-step explanation:

We can use the Central Limit Theorem to find the probability that the mean cholesterol level of the sample will be greater than 200.

Since the sample size is 20, which is greater than 30, we can assume that the sample mean follows a normal distribution.

To find the probability, we standardize the sample mean by subtracting the population mean and dividing by the population standard deviation:

Z = (200 - 191) / (22.4 / √20)

= 0.6711

Using a standard normal table or calculator, we find that the probability of Z being greater than 0.6711 is approximately 0.2524.

Therefore, the probability that the mean cholesterol level of the sample will be greater than 200 is approximately 0.2524.