Question

A manufacturing company wants to randomly sample customers about their satisfaction rating on products. The company will give a gift certificate worth​ $25 to every customer who completes the survey. How much will it cost the company to obtain a margin of error of plus or minus±​5%?

Answer 1

$10,000.

Explanation:

We have been given that a manufacturing company wants to randomly sample customers about their satisfaction rating on products. The company will give a gift certificate worth​ $25 to every customer who completes the survey. We are asked to find the amount that will cost the company to obtain a margin of error of plus or minus ±​5%.

We will use margin of error formula to solve our given problem.

`\text{Margin of error}=(1)/(√(n))`, where n represents sample size.

`5\%=(5)/(100)=0.05`

Our given margin of error is ±​5% or 0.05.

Let us solve for n.

`0.05=(1)/(√(n))`

`√(n)=(1)/(0.05)`

`√(n)=20`

Upon squaring both sides, we will get:

`(√(n))^2=20^2`

`n=400`

Therefore, the sample size is 400.

Since company will give a gift certificate worth​ $25 to every customer, so amount for giving gift certificates to 400 customers would be 400 times $25.

`400* \$25=\$10,000`

Therefore, it will cost $10,000 for the company to obtain a margin of error of ±​5%.