Stats: Sampling Distributions

Question

1. Human body temperatures are normally distributed with mean 98.2 degrees and standard deviation off 0.62 degrees. Use this information to find the following.

The probability that a randomly selected subject has a temperature between 98.1 and 98.5 degrees

Suppose a simple random sample of 25 is selected from the population of healthy adults: 

i) What is the mean of the sampling distribution of samples of size 25 taken from this population?

ii) What is the standard deviation of the sampling distribution of samples of size 25 taken from this population?

iii) How is this sampling distribution distributed?

Answer 1

i) The mean of a sampling distribution will be the same as the population. Therefore, the mean of the sampling distribution is also 98.2.

ii) For the standard deviation of the sampling distribution, use the formula σ/√n. In this problem, the sampling distribution is 0.62/√25 = 0.62/5 = 0.124

iii) Since the problem states that the original data is normally distributed, we know the sampling distribution will also be normally distributed no matter the sample size. The sampling distribution will be normally distributed with a mean of 98.2 and a standard deviation of 0.124.