A dishwasher has a mean life of 12 years with an estimated standard deviation of

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 10 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.) What is the shape of the sampling distribution of the sample mean? Why?

e.) Find the probability that the sample mean of the dishwashers is less than 6 years.

f.) If you found the sample mean life of the 10 dishwashers to be less than 6 years, would you think that you have a problem with the manufacturing process?   Why or why not?

Explanation / Answer

Ans:

a)Sample mean of samples of sizes 10

b)Mean=poplation mean=12

c)standard deviation=1.25/sqrt(10)=0.395

d)Normal distribution or bell shaped.

When we take samples from normal distribution,the sampling distribution of sample means follow normal distribution.

e)

z=(6-12)/(1.25/sqrt(10))

z=-15.18

P(z<-15.18)=0

f)No,as probability of finding sample mean less than 6 is approximately 0.

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