Question

In: Statistics and Probability

[1] The distribution of cholesterol levels of a population of 40-year-olds is approximately normally distributed with...

[1] The distribution of cholesterol levels of a population of 40-year-olds is approximately normally distributed with a mean of 220 mg/deciliter and a standard deviation of 12 mg/deciliter.

A. What is the approximate probability that a randomly selected 40-year-old from this population has a cholesterol level of more than 225 mg/deciliter? (Draw an appropriate diagram, find a z-score and indicate your calculator commands.)

B. A researcher takes a random sample of 16 people from this population and calculates the average cholesterol level.

i. What is the mean of the sampling distribution for a sample of this size? Briefly justify your answer.

ii. What is the standard deviation of the sampling distribution for a sample of this size? Briefly justify your answer.

iii. What is the shape of the sampling distribution for a sample of this size? Briefly justify your answer.

C. A researcher takes a random sample of 16 people from this population. What is the approximate probability that the sample mean cholesterol level for 16 random people will be greater than 225 mg/deciliter? (Draw an appropriate diagram, find a z-score and indicate your calculator commands.)

Expert Solution

Here it is given that distribution is normal with mean=220 and standard deviation=12

A. We need to find

As distribution is normal we can convert x to z

. We will find value using below table.

B. Now as population is normal, sample mean is also normal as per central limit theorem

i. Mean is

ii. Standard deviation is

iii. Distribution is normal as per central limit theorem and shape is bell.

c. Now we need to find

Converting it to z, we get

We have used above table again.

orchestra answered 1 year ago

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