Question

A dishwasher has a mean life of 12 years with an estimated standard deviation of 1.25 years ("Appliance life expectancy," 2013). Assume the life of a dishwasher is normally distributed. a.) State the random variable. b.) Find the probability that a dishwasher will last more than 15 years. c.) Find the probability that a dishwasher will last less than 6 years. d.) Find the probability that a dishwasher will last between 8 and 10 years. e.) If you found a dishwasher that lasted less than 6 years, would you think that you have a problem with the manufacturing process? Why or why not? f.) A manufacturer of dishwashers only wants to replace free of charge 5% of all dishwashers. How long should the manufacturer make the warranty period?

Answer 1

a)

random variable X is life of a randomely chosen dishwasher which is normally distributed with mean =12 years and std deviation =1.25 years.

b)

for normal distribution z score =(X-μ)/σx

probability =

P(X>15)

=

P(Z>2.4)=

1-P(Z<2.4)=

1-0.9918=

0.0082

c)

probability =

P(X<6)

=

P(Z<-4.8)=

0.0000

d)

probability =

P(8<X<10)

=

P(-3.2<Z<-1.6)=

0.0548-0.0007=

0.0541

e)

Yes as probability of that happening is very less

f)

for bottom 5% ; critical z =-1.645

therefore corresponsing warranty period =mean+z*Std deivaiton=12-1.645*1.25 =9.94 Years