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algol [13]
2 years ago
13

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
Mathematics
1 answer:
hjlf2 years ago
4 0

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.

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