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

Answer:

A sample size of 400 was used in the study.

Step-by-step 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) $s = \frac{\sigma}{\sqrt{n}}$.

In this problem, we have that:

$\sigma = 860, s = 43$

We have to find n.

$s = \frac{\sigma}{\sqrt{n}}$

$43 = \frac{860}{\sqrt{n}}$

$43\sqrt{n} = 860$

$\sqrt{n} = \frac{860}{43}$

$\sqrt{n} = 20$

$(\sqrt{n})^{2} = 20^{2}$

$n = 400$

A sample size of 400 was used in the study.