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An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed with a standard deviation of 45 hours. How large a sample is needed if we wish to be 98% confident that our sample mean will be within 14 hours of the true mean?

An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed with a standard deviation of 45 hours. How large a sample is needed if we wish to be 98% confident that our sample mean will be within 14 hours of the true mean?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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7. Please answer the following probability question.
**Sample Size Calculation for Light Bulb Manufacturing** An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed with a standard deviation of 45 hours. How large a sample is needed if we wish to be 98% confident that our sample mean will be within 14 hours of the true mean? In this educational scenario, we are tasked with determining the appropriate sample size to achieve a specified level of confidence in estimating the average lifespan of light bulbs. The standard deviation provided highlights the variability in bulb lifespans, and the confidence level of 98% ensures statistical reliability. The objective is to calculate the sample size necessary to achieve a margin of error of 14 hours.
Transcribed Image Text:**Sample Size Calculation for Light Bulb Manufacturing** An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed with a standard deviation of 45 hours. How large a sample is needed if we wish to be 98% confident that our sample mean will be within 14 hours of the true mean? In this educational scenario, we are tasked with determining the appropriate sample size to achieve a specified level of confidence in estimating the average lifespan of light bulbs. The standard deviation provided highlights the variability in bulb lifespans, and the confidence level of 98% ensures statistical reliability. The objective is to calculate the sample size necessary to achieve a margin of error of 14 hours.
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