Question

Consumer Reports indicated that the average life of a refridgerator before replacement is mean= 14 years with a (95% of data) range from 9 to 19 years. Let x= age at which refrigerator is replaced. Assume that x has a distribution that is approximately normal.

a) Find a good approximation for the standard deviation of x values.

b) What is the probability that someone will keep a refrigerator fewer than 11 years before replacement?

c) What is the probability that someone will keep a refrigerator more than 18 years before replacement?

d) Inverse Normal Distribution: Assume that the average life of a refrigerator is 14 years, with the standard deviation given in part (a) before it breaks. Suppose that a company guarantees refrigerators and will replace a refrigerator that breaks while under guarantee with a new one. However, the company does not want to replace more than 5% of the refrigerators under guarantee. For how long should the guarantee be made (rounded to the nearest tenth of a year)?

The resting heart rate for an adult horse should average about (mean= 46 beats per minute) with a (95% of data) range from 22 to 70 beats per minute, based on information from the Merck Veterinary Manual. Let x be a random variable that represents the resting heart rate for an adult horse. Assume that x has a distribution that is approximately normal.

a) Estimate the standard deviation of the x distribution.

b) What is the probability that the heart rate is fewer than 25 beats per minute?

c) What is the probability that the heart rate is greater than 60 beats per minute?

d) What is the probability that the heart rate is between 25 and 60 beats per minute?

e) Inverse Normal Distribution A horse whose resting heart rate is in the upper 10% of the probability distribution of heart rates may have a secondary infection or illness that needs to be treated. What is the heart rate corresponding to the upper 10% cutoff point of the probability distribution?

Answer #1

Consumer Reports indicated that the average life of a
refrigerator before replacement is 14 years with a (95% of data)
range from 9 to 19 years. Let x = age at which a refrigerator is
replaced. Assume that x has a distribution that is approximately
normal.
a. Find a good approximation for the standard deviation of x
values.
b. What is the probability that someone will keep a refrigerator
fewer than 11 years before replacement?
c. What is the probability...

According to the Merck Veterinary Manual, the resting heart
rate for an adult horse is about µ = 46 beats per minute with σ =
12 beats per minute. Let x be a random variable that
represents the resting heart rate for an adult horse. Consider
x to have a distribution that follows a normal
distribution. Answer the following questions. Recall the process to
derive an answer for finding probabilities and show each step of
your work for tractability purposes....

The resting heart rate for an adult horse should average about
μ = 42 beats per minute with a (95% of data) range from 18
to 66 beats per minute. Let x be a random variable that
represents the resting heart rate for an adult horse. Assume that
x has a distribution that is approximately normal.
(a) The empirical rule indicates that for a symmetrical and
bell-shaped distribution, approximately 95% of the data lies within
two standard deviations of the...

According to a Consumer Report, the mean replacement
time of a television is 8.2 years with a standard deviation of 1.1
years. The distribution of TV replacement times is approximately
Normal. Use a table or technology for each question. Include an
appropriately labeled Normal curve for each part. There should be
three separate curves.
What is the probability that a person will replace thei
According to a Consumer Report, the mean replacement
time of a television is 8.2 years with...

Suppose, household color TVs are replaced at an average age of
μ = 8.6 years after purchase, and the (95% of data) range
was from 6.0 to 11.2 years. Thus, the range was 11.2 – 6.0 = 5.2
years. Let x be the age (in years) at which a color TV is
replaced. Assume that x has a distribution that is
approximately normal.
(a) The empirical rule indicates that for a symmetrical and
bell-shaped distribution, approximately 95% of the data...

Suppose, household color TVs are replaced at an average age of
μ = 7.4 years after purchase, and the (95% of data) range
was from 5.0 to 9.8 years. Thus, the range was 9.8 − 5.0 = 4.8
years. Let x be the age (in years) at which a color TV is
replaced. Assume that x has a distribution that is
approximately normal.
(a) The empirical rule indicates that for a symmetric and
bell-shaped distribution, approximately 95% of the data...

Suppose, household color TVs are replaced at an average age of μ
= 9.0 years after purchase, and the (95% of data) range was from
6.4 to 11.6 years. Thus, the range was 11.6 − 6.4 = 5.2 years. Let
x be the age (in years) at which a color TV is replaced. Assume
that x has a distribution that is approximately normal. (a) The
empirical rule indicates that for a symmetric and bell-shaped
distribution, approximately 95% of the data...

Suppose, household color TVs are replaced at an average age of
μ = 7.8 years after purchase, and the (95% of data) range
was from 5.4 to 10.2 years. Thus, the range was 10.2 − 5.4 = 4.8
years. Let x be the age (in years) at which a color TV is
replaced. Assume that x has a distribution that is
approximately normal.
(a) The empirical rule indicates that for a symmetric and
bell-shaped distribution, approximately 95% of the data...

Suppose, household color TVs are replaced at an average age of μ
= 8.2 years after purchase, and the (95% of data) range was from
4.2 to 12.2 years. Thus, the range was 12.2 − 4.2 = 8.0 years. Let
x be the age (in years) at which a color TV is replaced. Assume
that x has a distribution that is approximately normal.
(a) The empirical rule indicates that for a symmetric and
bell-shaped distribution, approximately 95% of the data...

Every day for a year, before you get out of bed you measure and
record your resting heart rate. The data is normally distributed
with a mean of 56 beats per minute and a standard deviation of 5
beats per minute.
a) What is the probability that your resting heart rate will be
between 50 and 60 bpm?
b) What percentage of the year will your resting heart rate be
above 54 bpm? How many days is that?
c) What...

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