Question 1203821: Company XYZ know that replacement times for the quartz time pieces it produces are normally distributed with a mean of 15.9 years and a standard deviation of 1.4 years. Find the probability that a randomly selected quartz time piece will have a
replacement time less than 12.1 years? If the company wants to provide a warranty so that only 0.9% of the quartz time pieces will be replaced before the warranty expires, what is the time length of the warranty?
Answer by ikleyn(52778)   (Show Source):
You can put this solution on YOUR website! .
Company XYZ  knows that replacement times for the quartz time pieces it produces
are normally distributed with a mean of 15.9 years and a standard deviation of 1.4 years.
(a) Find the probability that a randomly selected quartz time piece will have a
replacement time less than 12.1 years?
(b) If the company wants to provide a warranty so that only 0.9% of the quartz time pieces
will be replaced before the warranty expires, what is the time length of the warranty?
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(a) In part (a), they want you determine the probability that a randomly selected quartz
time piece will have a replacement time less than 12.1 years.
It is the same as to determine the area under the given normal curve
on the left of the time mark of 12.1 year.
Use the standard function normalcdf of your regular calculator TI-83/84
z1 z2 mean SD <<<---=== formatting pattern
P = normalcdf(-9999, 12.1, 15.9, 1.4)
You will get the value P = 0.0033 (rouned). ANSWER
Alternatively, you may use free of charge online calculator at this web-site
https://davidmlane.com/hyperstat/z_table.html
(use it in the mode "Area from a value").
It has clearly designed interface, so even a beginner student can learn it and use easily.
Online calculator will give you the same answer.
(b) In part (b), they want you determine the time mark on the number line such that
only 0.9% = 0.009 of the quartz time pieces will be replaced before the warranty expires.
It is the same as to determine the time mark on the number line such that
the area under the normal curve on the left of this mark would be 0.009.
Use the standard function invNorm of your regular calculator TI-83/84
area mean SD <<<---=== formatting pattern
years = invNorm(0.009, 15.9, 1.4)
You will get the value years = 13.534, or 13.5 years, rounded. ANSWER
Alternatively, you may use the same free of charge online calculator at this web-site
https://davidmlane.com/hyperstat/z_table.html
(this time use it in the mode "Value from an area").
It has clearly designed interface, so even a beginner student can learn it and use easily.
Online calculator will give you the same answer.
Solved.
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