Company XYZ know that replacement times for the quartz time pieces it produces a

Question

Company XYZ know that replacement times for the quartz time pieces it produces are normally distributed with a mean of 14.8 years and a standard deviation of 2.1 years. Enter your answer accurate to 4 decimal places. a. Find the probability that a randomly selected quartz time piece will have a replacement time less than 9.97 years? Pix 9.97 years)- b. If the company wants to provide a warranty so that only 2.7% of the quartz time pieces will be replaced before the warranty expires, what is the time length of the warranty? warranty- years

Explanation / Answer

a)

mean = 14.8 , sd = 2.1

Z = (X - mean)/sd

P(X < 9.97)

= P(Z < ( 9.97 - 14.8)/2.1))

= P(Z < -2.3)

= 0.0107

b)

P(Z < z*) = 0.027

z* = -1.927

hence

X = 14.8 -2.927 * 2.1 = 8.6533

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