You are the operations manager for an airline and you are considering a higher fare level for passengers in aisle seats. How many randomly selected air passengers must you survey? Assume that you want to be 95% confident that the sample percentage is within 4.2 percentage points of the true population percentage.

545 randomly selected air passengers must be surveyed.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.

In which

z is the zscore that has a pvalue of .

The margin of error is:

95% confidence level

So , z is the value of Z that has a pvalue of , so .

Assume that you want to be 95% confident that the sample percentage is within 4.2 percentage points of the true population percentage.

We dont know the true proportion, so we use , which is when the largest sample size will be needed. We have to find n for which . So

Rouding up

545 randomly selected air passengers must be surveyed.

it's

what shape is