Question

The average lifespan of a CleanFreek dishwasher is normally distributed with a mean of 8 years and a standard deviation of 1.5 years.

Standard Normal Distribution Table

a. What is the probability that a CleanFreek dishwasher will last longer than 12 years?
P(X > 12)=P(X > 12)=

b. What is the probability that a CleanFreek dishwasher will last fewer than 7 years?
P(X < 7)=P(X < 7)=

c. What length warranty should be established on the dishwashers so that no more than 1.7% of the units will need to be replaced under warranty?
x=x=

years

Round to 2 decimal places.

h(i,x)=

{10if  program i halts on input x,otherwise.{1if  program i halts on input x,0otherwise.

Answer 1

We are given the distribution here as:

a) The probability here is computed as:
P(X > 12)

Converting it to a standard normal variable, we have here:

Getting it from the standard normal tables, we have here:

therefore 0.0038 is the required probability here.

b) The probability here is computed as:

P(X < 7)

Converting it to a standard normal variable, we have here:

Getting it from the standard normal tables, we have here:

Therefore 0.2525 is the required probability here.

c) From standard normal tables, we have here:
P(Z < -2.120) = 0.017

Therefore the life length here is computed as:
= Mean -2.120*std Dev

= 8 -2.120*1.5

= 4.82

Therefore 4.82 years is the required cutoff value here.