Question

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?

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

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 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 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 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 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 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 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 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 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 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...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 37 minutes ago

asked 37 minutes ago

asked 51 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago