Question

Credit card balances follow a nearly normal distribution with a mean of $2,900 and a standard deviation of $860. A local credit union believes their customers are carrying an above average credit card balance, so they carry out a study to determine their customers' debt. If the study results in a standard error of $43, what sample size was used in the study

Answer 1

A sample size of 400 was used in the study.

Explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean
`\mu` and standard deviation
`\sigma`, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
`\mu` and standard deviation(standard error)
`s = (\sigma)/(√(n))`.

In this problem, we have that:

`\sigma = 860, s = 43`

We have to find n.

`s = (\sigma)/(√(n))`

`43 = (860)/(√(n))`

`43√(n) = 860`

`√(n) = (860)/(43)`

`√(n) = 20`

`(√(n))^(2) = 20^(2)`

`n = 400`

A sample size of 400 was used in the study.