The owner of a shopping mall wants an estimate of the lengthof
time shoppers spend in the mall. the estimate is to be within
5minutes of the true time, with a 98% confidence level. the
estimateof the standard deviation of the length of time spent in
the mallis 20 minutes. how large a sample will be needed?

A sample size of at least 87 will be needed.

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 M as such

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

In this problem, we have that:

So

A sample size of at least 87 will be needed.