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# 6. A dishwasher has a mean life of 10 years with an estimated standard deviation of 1.25 years. 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?

7. A dishwasher has a mean life of 10 years with an estimated standard deviation of 1.05 years. 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?

1) a) X is a normal distribution b) The probability is 0 c) The probability is 0.0007 d) The probability is 0.4452 e)... View the full answer

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