Question

A dishwasher has a mean life of 12 years with an estimated standard deviation of 1.25 years ("Appliance life expectancy," 2013). The life of a dishwasher is normally distributed. Suppose you are a manufacturer and you take a sample of 25 dishwashers that you made.

a.)     State the random variable.

b.)    Find the mean of the sample mean.

c.)     Find the standard deviation of the sample mean.

d.)    Find the probability that the sample mean of the dishwashers is less than 8 years.

Answer 1

SolutionA:

Random variable is  The life of a dishwasher

b.)    Find the mean of the sample mean.

Random variable follows normal distribution

sample mean=population mean=12 years

sample mean=12 years

Solutionc:

c.)     Find the standard deviation of the sample mean

standard deviation of the sample mean=population std dev/sqrt(sample size)

=1.25/sqrt(25)

=0.25

standard deviation of the sample mean=0.25

d.)    Find the probability that the sample mean of the dishwashers is less than 8 years.

P(Xbar <8)

Z=x-mean/s

=8-12/0.25

Z=-16

P(Z<-16)

= 6.388754e-58

=0.0000

the probability that the sample mean of the dishwashers is less than 8 years=0.0000