Question

Company XYZ know that replacement times for the DVD players it produces are normally distributed with a mean of 5.8 years and a standard deviation of 0.9 years.

Find the probability that a randomly selected DVD player will have a replacement time less than 4 years?
P(X < 4 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 3.6% of the DVD players 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

µ = 5.8

sd = 0.9

a)

                          

                           = P(Z < -2)

                           = 0.0228 (ans)

b)

or, x = 5.8 + 1.799 * 0.9

or, x = 7.4 (ans)