Question

The average life expectancy of people in the united states in 2018 was 78.54 years with a standard deviation of approximately 15 years

Answer 1

Question:

The average life expectancy of people in the United States in 2018 was 78.54 years with a standard deviation of approximately 15 years.

Suppose we take a sample of 40 individuals in the United States, what are the mean and standard deviation for sample averages from samples of size 40?

Answer:

`\bar x = 78.54`

`\sigma_x = 2.37`

Explanation:

Given

`\mu = 78.54` --- Population mean

`\sigma = 15` --- Population standard deviation

`n = 40` --- Sample size

Solving (a): The sample mean

According to the central limit theorem, sample mean is always equal to the population mean.

So:

`\bar x = 78.54`

Solving (b): The sample standard deviation

Using the central limit theorem, we have:

`\sigma_x = (\sigma)/(\sqrt n)`

So:

`\sigma_x = (15)/(√(40))`

`\sigma_x = (15)/(6.32)`

`\sigma_x = 2.37`