Question

A company knows that replacement times for the quartz time pieces it produces are Normally distributed with a mean of 12.8 years and a standard deviation of 2.2 years.

Find the proportion of a randomly selected quartz time pieces that will have a replacement time less than 5.8 years?
P(X < 5.8 years) =

Enter your answer accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

If the company wants to provide a warranty so that only 1% of the quartz time pieces will be replaced before the warranty expires, what is the time length of the warranty?
warranty = years

Enter your answer as a number accurate to 1 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Answer 1

Solution :

Given that ,

mean = = 12.8

standard deviation = = 2.2 P(x < 5.8) = P[(x - ) / < (5.8 -12.8)/2.2 ]

= P(z < -3.182) = 0.0007

Probability = 0.0007

- Using standard normal table ,

P(Z < z) = 1%

P(Z < z) = 0.01

P(Z < -2.326) = 0.01

z = -2.326

Using z-score formula,

x = z * +

x = -2.326 * 2.2 + 12.8 = 7.7

warranty = 7.7 years