Question

A dishwasher has a mean life of 12 years with an estimated standard deviation of 1.25...

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?

Homework Answers

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

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A dishwasher has a mean life of 12 years with an estimated standard deviation of 1.25...
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. State the random variable. Find the probability that a dishwasher will last more than 15 years. Find the probability that a dishwasher will last less than 6 years. Find the probability that a dishwasher will last between 8 and 10 years. If you found a dishwasher that lasted less than...
A dishwasher has a mean life of 12 years with an estimated standard deviation of 1.25...
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. State the random variable. Find the mean of the sample mean. Find the standard deviation of the sample mean. What is the shape of the sampling distribution of the sample mean? Why? Find the probability...
A dishwasher has a mean life of 12 years with an estimated standard deviation of 1.25...
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. State the random variable. Find the mean of the sample mean. Find the standard deviation of the sample mean. What is the shape of the sampling distribution of the sample mean? Why? Find the probability...
A dishwasher has a mean life of 12 years with an estimated standard deviation of 1.25...
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?...
A dishwasher has a mean life of 12 years with an estimated standard deviation of 1.25...
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...
A dishwasher has a mean life of 10 years with an estimated standard deviation of 1.05...
A dishwasher has a mean life of 10 years with an estimated standard deviation of 1.05 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. State the random variable. Find the mean of the sample mean. Find the standard deviation of the sample mean. What is the shape of the sampling distribution of the sample mean? Why? Find the probability...
The average life expectancy of dishwashers produced by a company is 6 years with a standard...
The average life expectancy of dishwashers produced by a company is 6 years with a standard deviation of 8 months. Assume that the lives of dishwashers are normally distributed. A.What is the probability that a randomly selected dishwasher will have a life expectancy of at least 7 years? B.Dishwashers that fail operating in less than 4 ½ years will be replaced free of charge. What percent of dishwashers are expected to be replaced free of charge? C.What are the minimum...
The average lifespan of a CleanFreek dishwasher is normally distributed with a mean of 8 years...
The average lifespan of a CleanFreek dishwasher is normally distributed with a mean of 8 years and a standard deviation of 1.8 years. Standard Normal Distribution Table a. What is the probability that a CleanFreek dishwasher will last longer than 12 years? P(X > 12)= 0 b. What is the probability that a CleanFreek dishwasher will last fewer than 6 years? P(X < 6)= 0 c. What length warranty should be established on the dishwashers so that no more than...
The average lifespan of a CleanFreek dishwasher is normally distributed with a mean of 8 years...
The average lifespan of a CleanFreek dishwasher is normally distributed with a mean of 8 years and a standard deviation of 1.9 years.a. What is the probability that a CleanFreek dishwasher will last longer than 10 years? P(X > 10)= b. What is the probability that a CleanFreek dishwasher will last fewer than 7 years? P(X < 7)= c. What length warranty should be established on the dishwashers so that no more than 1.6% of the units will need to...
A) The mean lifetime of a smartphone model is 3 years with a standard deviation of...
A) The mean lifetime of a smartphone model is 3 years with a standard deviation of 5 months. Assume normal distribution. What percentage of all smartphones should the manufacturer expect to replace if they offer a warranty period of 30 months? B) The mean lifetime of a smartphone model is 3 years with a standard deviation of 5 months. Assume that lifetimes are normally distributed. The CEO wants to budget for replacing not more than 5% of the smartphones during...