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Light bulbs used for the exterior walkways at MJC's west campus have an average lifetime of 500 hours. Assume that the lifetime of bulbs is normally distributed with a standard deviation 50 hours. Suppose all of the bulbs were replaced at the same time and they have been turned on for a total of 550 hours. What is the probability that a randomly chosen light bulb lasts less than 550 hours?

Light bulbs used for the exterior walkways at MJC's west campus have an average lifetime of 500 hours. Assume that the lifetime of bulbs is normally distributed with a standard deviation 50 hours. Suppose all of the bulbs were replaced at the same time and they have been turned on for a total of 550 hours. What is the probability that a randomly chosen light bulb lasts less than 550 hours?

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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**Light bulbs used for the exterior walkways at MJC's west campus have an average lifetime of 500 hours. Assume that the lifetime of bulbs is normally distributed with a standard deviation of 50 hours. Suppose all of the bulbs were replaced at the same time and they have been turned on for a total of 550 hours. What is the probability that a randomly chosen light bulb lasts less than 550 hours?** **Explanation for an Educational Website:** This problem involves the concept of normal distribution which is often used in statistics to describe how data points are spread around a mean. In this scenario, the lifetimes of light bulbs are normally distributed. - **Mean (average) lifetime**: 500 hours - **Standard deviation**: 50 hours - **Time they have been turned on**: 550 hours To solve this problem, you would calculate the probability that a light bulb lasts less than 550 hours by using the properties of the normal distribution. Specifically, you would find the Z-score for 550 hours and then use a standard normal distribution table or software to find the corresponding probability.
Transcribed Image Text:**Light bulbs used for the exterior walkways at MJC's west campus have an average lifetime of 500 hours. Assume that the lifetime of bulbs is normally distributed with a standard deviation of 50 hours. Suppose all of the bulbs were replaced at the same time and they have been turned on for a total of 550 hours. What is the probability that a randomly chosen light bulb lasts less than 550 hours?** **Explanation for an Educational Website:** This problem involves the concept of normal distribution which is often used in statistics to describe how data points are spread around a mean. In this scenario, the lifetimes of light bulbs are normally distributed. - **Mean (average) lifetime**: 500 hours - **Standard deviation**: 50 hours - **Time they have been turned on**: 550 hours To solve this problem, you would calculate the probability that a light bulb lasts less than 550 hours by using the properties of the normal distribution. Specifically, you would find the Z-score for 550 hours and then use a standard normal distribution table or software to find the corresponding probability.
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