Question

According to recent studies, cholesterol levels in healthy adults average about 215 mg/dL with a standard deviation of about 34 mg/dL and are roughly normally distributed. Suppose we collect a random sample of 45 healthy adults and measure their cholesterol level. What is the standard deviation of the distribution of sample average (sampe size 45)?

Note:
1- Round any intermediate numbers to 3 decimal places.
2- Round your final answer to 3 decimal places. Enter your final answer with 3 decimal places.

Answer 1

The standard deviation of the distribution of sample mean, also known as the standard error, for the given population standard deviation of 34 mg/dL and sample size of 45 is 5.067 mg/dL.

Step-by-step explanation:

When dealing with the distribution of sample means, the standard deviation of the distribution (also known as the standard error) can be calculated using the formula σ/√n, where σ is the population standard deviation and n is the sample size. In this case, the population standard deviation is 34 mg/dL, and the sample size is 45.

To calculate the standard error (the standard deviation of the sampling distribution of the sample mean), we use the following steps:

1. Identify the population standard deviation (σ), which is 34 mg/dL.
2. Identify the sample size (n), which is 45.
3. Apply the formula σ/√n to find the standard error. So, Standard Error (SE) = 34/√45.

Calculating the standard error gives us SE = 34/√45 = 34/6.708 = 5.067 mg/dL. Rounded to three decimal places, the standard error is 5.067 mg/dL.