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%?

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.

[tex]\text{Margin of error}=\frac{1}{\sqrt{n}}[/tex], where n represents sample size.

[tex]5\%=\frac{5}{100}=0.05[/tex]

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

Let us solve for n.

[tex]0.05=\frac{1}{\sqrt{n}}[/tex]

[tex]\sqrt{n}=\frac{1}{0.05}[/tex]

[tex]\sqrt{n}=20[/tex]

Upon squaring both sides, we will get:

[tex](\sqrt{n})^2=20^2[/tex]

[tex]n=400[/tex]

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.

[tex]400\times \$25=\$10,000[/tex]

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

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%?

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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%?