Question 7(10 points)

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.)True or False: The random variablexdefines the life expectancy of a dishwasher

b.)Find the probability that a dishwasher will last more than 15 years.

c.)Find the probability that a dishwasher will last less than 8 years.

d.)Find the probability that a dishwasher will last between 8 and 10 years.

e.)A manufacturer of dishwashers only wants to replace free of charge 5% of all dishwashers.How long should the manufacturer make the warranty period?

For part (a):EnterTRUEorFALSE

For parts (b) through (d):Enter answers in decimal form rounded to nearest ten-thousandth (4 places after decimal). Examples of correctly entered answers:

0.00000.00030.00700.01000.40000.66511.0000

For part (e):Enter answer rounded to nearest whole number of year(s).Do not include units of time.

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Question 8(10 points)

A random variable is normally distributed.It has a mean of 245 and a standard deviation of 21.

a.)For a sample of size 10, state the mean of the sample mean.

b.)For a sample of size 10, state the standard deviation of the sample mean (the "standard error of the mean").

c.)For a sample of size 35, state the mean of the sample mean.

d.)For a sample of size 35, state the standard deviation of the sample mean (the "standard error of the mean").

e.)TRUE or FALSE:As sample size increases, standard deviation of the sample mean (the "standard error of the mean") also increases.

For parts (a) through (d), enter answer in decimal form rounded to nearest thousandth (3 places after decimal).Examples of correctly entered answers: 0.0000.0040.0801.2000.59413.000

For part (e):EnterTRUEorFALSE

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Question 9(10 points)

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.)TRUE or FALSE:The random variable is defined as thesumof dishwasher life expectancies in the sample.

b.)For a sample of size 10, state the mean of the sample mean.

c.)For a sample of size 10, state the standard deviation of the sample mean (the "standard error of the mean").

d.)Suppose a sample of size 10 is taken.Find the probability that the sample mean dishwasher life expectancy is less than 11 years.

For part (a):Enter TRUE or FALSE

For parts (b) through (d), enter answer in decimal form rounded to nearest thousandth (3 places after decimal).Examples of correctly entered answers:0.0000.0040.0801.2000.59413.000

Question 9 options:

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Question 10(10 points)

The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 36 and a standard deviation of about ten. Suppose that 16 individuals are randomly chosen.

a.)TRUE or FALSE:The random variable is defined as theaveragepercent of fat calories consumed each day by a person in America.

b.)For a sample of size 16, state the mean of the sample mean.

c.)For a sample of size 16, state the standard deviation of the sample mean (the "standard error of the mean").

d.)Suppose a sample of size 16 is taken.Find the probability that the average percent of fat calories consumed ismore than30.

For part (a):EnterTRUEorFALSE

For parts (b) through (d), enter answer in decimal form rounded to nearest thousandth (3 places after decimal).Examples of correctly entered answers:0.0000.0040.0801.2000.59413.000

Question 10 options: