Clarence wants to estimate the percentage of students who live more than three miles from the school. he wants to create a 98% confidence interval which has an error bound of at most 4%. how many students should be polled to create the confidence interval?

Clarence should poll 847 to create the confidence interval.

Step-by-step explanation:

We have the following information:

1-α = 0.98

e = 0.04

p = unknown

The value of the sample (n) can be calculated using the following formula:

First step: obtain the value of p

Since we're not given a value of p, we'll have to use the value that maximizes the sample. The value that maximizes the sample is always p = 0.5.

Second step: obtain the value of z

Since the confidence interval is going to be of 98%, you’ll have 1% of the distribution in each tail. Therefore the z values we’re looking for are the cumulative values of the z distribution up to 1% or up to 99%. Either value will work, but you’ll just need to use one of them.

Looking up on any z-table, the value of a 99% area in a z distribution is of z = 2.327.

Third step: replace in the formula

Since we're looking for the number of people that should be polled, we cannot have decimals in the answer. Therefore we round up to 847 students.

answer: t=3

step-by-step explanation: