Question

A box of tickets has an average of 420; the SD is 84. If we draw at random (with replacement) 50 times and compute the average of the draws, the expected value of the average of the draws equals 420 and the standard error of the average of the draws equals ____. (Enter correct to two decimal places.)

Answer 1

Average of the draws equals 420

Standard Error = 11.88

Explanation:

Given

`\mu = 420`

`\sigma = 84`

`n =50`

Solving (a): The average of the draws

This implies that we calculate the sample mean

This is calculated as:

`\bar x = \mu` --- Sample Mean = Population Mean

So, we have:

`\bar x = 420`

Solving (b): The standard error

This is calculated as:

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

So, we have:

`SE=\frac{84}{\sqrt {50}}`

Using the calculator, we have:

`SE=11.88`