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Company XYZ knows that replacement times for the mircowaves it produces are normally distributed with a mean of 15.3 years and a standard deviation of 1.3 years. Let X be the replacement time of a randomly selected mircowave. a. What is the distribution of X? X-NV Please show the following answers to 4 decimal places. b. If a mircowave is randomly chosen, find the probability that it will be replaced in at most 18 years. 0.9811✔ Or 15.3 1.3 c. If a mircowave is randomly chosen, find the probability that it will be replaced between 12.6 and 14.8 years. 0.3314✓ Please show the following answer to 1 decimal place. d. If the company wants to provide a warranty so that only 7% of the mircowaves will be replaced before the warranty expires, what is the time length of the warranty? years

Company XYZ knows that replacement times for the mircowaves it produces are normally distributed with a mean of 15.3 years and a standard deviation of 1.3 years. Let X be the replacement time of a randomly selected mircowave. a. What is the distribution of X? X-NV Please show the following answers to 4 decimal places. b. If a mircowave is randomly chosen, find the probability that it will be replaced in at most 18 years. 0.9811✔ Or 15.3 1.3 c. If a mircowave is randomly chosen, find the probability that it will be replaced between 12.6 and 14.8 years. 0.3314✓ Please show the following answer to 1 decimal place. d. If the company wants to provide a warranty so that only 7% of the mircowaves will be replaced before the warranty expires, what is the time length of the warranty? years

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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**Normal Distribution of Microwave Replacement Times** Company XYZ recognizes that the replacement times for the microwaves it produces are normally distributed, with a mean of 15.3 years and a standard deviation of 1.3 years. Let X represent the replacement time of a randomly selected microwave. **a. Distribution of X** The distribution of X is given as \( X \sim N(15.3, 1.3) \). **Please show the following answers to 4 decimal places.** **b. Probability of Replacement in at Most 18 Years** If a microwave is chosen at random, the probability that it will be replaced in at most 18 years is 0.9811. **c. Probability of Replacement Between 12.6 and 14.8 Years** If a microwave is chosen at random, the probability that it will be replaced between 12.6 and 14.8 years is 0.3314. **Please show the following answer to 1 decimal place.** **d. Warranty Length for 7% Replacement Rate** If the company wants to provide a warranty such that only 7% of the microwaves will be replaced before the warranty expires, the time length of the warranty is _____ years.
Transcribed Image Text:**Normal Distribution of Microwave Replacement Times** Company XYZ recognizes that the replacement times for the microwaves it produces are normally distributed, with a mean of 15.3 years and a standard deviation of 1.3 years. Let X represent the replacement time of a randomly selected microwave. **a. Distribution of X** The distribution of X is given as \( X \sim N(15.3, 1.3) \). **Please show the following answers to 4 decimal places.** **b. Probability of Replacement in at Most 18 Years** If a microwave is chosen at random, the probability that it will be replaced in at most 18 years is 0.9811. **c. Probability of Replacement Between 12.6 and 14.8 Years** If a microwave is chosen at random, the probability that it will be replaced between 12.6 and 14.8 years is 0.3314. **Please show the following answer to 1 decimal place.** **d. Warranty Length for 7% Replacement Rate** If the company wants to provide a warranty such that only 7% of the microwaves will be replaced before the warranty expires, the time length of the warranty is _____ years.
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