High School

We appreciate your visit to A manufacturer of NFL regulation footballs uses a machine to inflate its new balls to a pressure of 13 5 pounds σ 0 1 When. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

A manufacturer of NFL regulation footballs uses a machine to inflate its new balls to a pressure of 13.5 pounds (σ = 0.1). When the machine is properly calibrated, the mean inflation pressure is 13.5 pounds, but uncontrollable factors can cause the pressure of individual footballs to vary. For quality control purposes, the manufacturer wishes to estimate the mean inflation pressure to within 0.025 pounds of its true value with 99 percent confidence. What sample size should be used?

Answer :

Final answer:

To estimate the mean inflation pressure to within 0.025 pounds with 99 percent confidence, the manufacturer should use a sample size of 107 footballs, calculated using the Z-score for a 99% confidence level and the given standard deviation of 0.1.

Explanation:

To determine the necessary sample size for the manufacturer's quality control procedures, we use the formula for estimating the sample size in a normal distribution:

n = (Z*σ/E)²

Where:

  • ‘n’ is the sample size needed
  • ‘Z’ is the Z-score corresponding to the desired confidence level
  • ‘σ’ is the population standard deviation
  • ‘E’ is the margin of error

Given a 99% confidence level, we look up the Z-score, which is approximately 2.576. The standard deviation (σ) is given as 0.1 pounds, and the desired margin of error (E) is 0.025 pounds.

Plugging those values into the formula, we get:

n = (2.576 * 0.1 / 0.025)²

Performing the calculations:

n = (2.576 * 4)²
= (10.304)²
= 106.232

We round up to the next whole number. Therefore, the manufacturer should use a sample size of 107 footballs to estimate the mean inflation pressure to within 0.025 pounds with 99 percent confidence.

Learn more about Sample Size Estimation here:

https://brainly.com/question/30885988

#SPJ11

Thanks for taking the time to read A manufacturer of NFL regulation footballs uses a machine to inflate its new balls to a pressure of 13 5 pounds σ 0 1 When. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada