A researcher is interested to determine the average age at which people obtain their first credit card. If past information shows a mean of 22 years and a standard deviation of 2 years, what size sample should be taken so that at 95% confidence the margin of error will be 3 months or less?

The sample size should be of at least 246.

Step-by-step explanation:

We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Ztable as such z has a pvalue of .

So it is z with a pvalue of , so

The margin of error M is

In which is the standard deviation of the population and n is the size of the sample.

In this problem, we have that:

We want the margin of error to be of 3 months. However the standard deviation is in years. So the margin of error must be in years. So M = 3/12 = 0.25.

As n increases, the margin of error decreases. So we need a sample of size at least n when M = 0.25.

The sample size should be of at least 246.

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step-by-step explanation: