Company XYZ knows that replacement times for the mircowaves it produces are normally distributed with a mean of 4.5 years and a standard deviation of 2 years. Let X be the replacement time of a randomly selected mircowave. a. What is the distribution of X? X - ? ✓ 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 less than 2.5 years. c. If a mircowave is randomly chosen, find the probability that it will be replaced between 4.1 and 8.1 years. Please show the following answer to 1 decimal place. d. If the company wants to provide a warranty so that only 8% of the mircowaves will be replaced before the warranty expires, what is the time length of the warranty? years

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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Company XYZ knows that replacement times for the mircowaves it produces are normally distributed with a
mean of 4.5 years and a standard deviation of 2 years. Let X be the replacement time of a randomly
selected mircowave.
a. What is the distribution of X?X - ? (
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 less than 2.5 years.
c. If a mircowave is randomly chosen, find the probability that it will be replaced between 4.1 and 8.1
years.
Please show the following answer to 1 decimal place.
d. If the company wants to provide a warranty so that only 8% of the mircowaves will be replaced
before the warranty expires, what is the time length of the warranty?
years
Transcribed Image Text:Company XYZ knows that replacement times for the mircowaves it produces are normally distributed with a mean of 4.5 years and a standard deviation of 2 years. Let X be the replacement time of a randomly selected mircowave. a. What is the distribution of X?X - ? ( 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 less than 2.5 years. c. If a mircowave is randomly chosen, find the probability that it will be replaced between 4.1 and 8.1 years. Please show the following answer to 1 decimal place. d. If the company wants to provide a warranty so that only 8% of the mircowaves will be replaced before the warranty expires, what is the time length of the warranty? years
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Calculus For The Life Sciences
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ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,