Question

The average lifespan of a CleanFreek dishwasher is normally distributed with a mean of 8 years and a standard deviation of 1.8 years. Standard Normal Distribution Table a. What is the probability that a CleanFreek dishwasher will last longer than 12 years? P(X > 12)= 0 b. What is the probability that a CleanFreek dishwasher will last fewer than 6 years? P(X < 6)= 0 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= 0.00 years

Answer 1

Solution :

Given that ,

mean = = 8 years

standard deviation = = 1.8 years

a) P(x > 12) = 1 - p( x< 12)

=1- p P[(x - ) / < (12 - 8) / 1.8 ]

=1- P(z < 2.22)

Using z table,

= 1 - 0.9868

= 0.0132

b) P(x < 6)

= P[(x - ) / < (6 - 8) /1.8 ]

= P(z < -1.11)

Using z table,

= 0.1335

c) Using standard normal table,

P(Z < z) = 1.6%

= P(Z < z ) = 0.016

= P(Z < -2.14 ) = 0.016  

z = -2.14

Using z-score formula,

x = z * +

x = -2.14 * 1.8 + 8

x = 4.15 years