Question

Question 2 (1 point) 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.) True or False: The random variable x defines the life expectancy of a dishwasher b.) Find the probability that a dishwasher will last more than 15 years. c.) Find the probability that a dishwasher will last less than 8 years. d.) Find the probability that a dishwasher will last between 8 and 10 years. e.) A manufacturer of dishwashers only wants to replace free of charge 5% of all dishwashers. How long should the manufacturer make the warranty period? For part (a): Enter TRUE or FALSE For parts (b) through (d): Enter answers in decimal form rounded to nearest ten- thousandth (4 places after decimal). Examples of correctly entered answers: 0.0000 0.0003 0.0070 0.0100 0.4000 0.6651 1.0000 For part (e): Enter answer rounded to nearest whole number of year(s). Do not include units of time.

Answer 1

a)

true

b)

probability =P(X>15)=P(Z>(15-12)/1.25)=P(Z>2.4)=1-P(Z<2.4)=1-0.9918=0.0082

c)

probability =P(X<8)=(Z<(8-12)/1.25)=P(Z<-3.2)=0.0007

d)

probability =P(8<X<10)=P((8-12)/1.25)<Z<(10-12)/1.25)=P(-3.2<Z<-1.6)=0.0548-0.0007=0.0541

e)

for 5th percentile critical value of z=		-1.645
therefore corresponding value=mean+z*std deviation=			9.9438~ 10 years