Question

The average lifespan of a CleanFreek dishwasher is normally distributed with a mean of 8 years and a standard deviation of 1.9 years.a. What is the probability that a CleanFreek dishwasher will last longer than 10 years?
P(X > 10)=

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

c. What length warranty should be established on the dishwashers so that no more than 1.6% of the units will need to be replaced under warranty?
x=

years

Round to 2 decimal places.

Answer 1

Solution :

Given ,

mean = = 8

standard deviation = = 1.9

P(x >10 ) = 1 - P(x<10 )

= 1 - P[(x -) / < (10-8) / 1.9]

= 1 - P(z <1.05 )

Using z table

= 1 - 0.8531

= 0.1469

B.

Solution :

Given ,

P(x<7 )

= P[(x -) / < (7-8) /1.9 ]

= P(z <-0.53 )

Using z table

= 0.2981

C.

Using standard normal table,

P(Z < z) = 1.6%

=(Z < z) = 0.016

= P(Z < z ) = 0.016

z = -2.14

Using z-score formula  

x = z +

x = -2.14 *1.9+8

x = 3.93