Suppose that a marketing research firm wants to conduct a survey to estimate the meanμof the distribution of the amount spent on entertainment by each adult who visits a certain popularresort. the firm would like to estimate the mean of this distribution to within $60 with 95% confidence. from data regarding past operations at the resort, it has been estimated that the standard deviation ofthe entertainment expenditures is no more than $400. how large does the firm’s sample size need to be?

The firm's sample size must be of at least 171 adults.

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

Now, find the margin of error M as such

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

In this problem, we have that:

. So

The firm's sample size must be of at least 171 adults.

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step-by-step explanation: