Question

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 lies within two standard deviations of the mean. Therefore, a 95% range of data values extending from μ − 2σ to μ + 2σ is often used for "commonly occurring" data values. Note that the interval from μ − 2σ to μ + 2σ is 4σ in length. This leads to a "rule of thumb" for estimating the standard deviation from a 95% range of data values. Estimating the standard deviation For a symmetric, bell-shaped distribution, standard deviation ≈ range 4 ≈ high value − low value 4 where it is estimated that about 95% of the commonly occurring data values fall into this range. Use this "rule of thumb" to approximate the standard deviation of x values, where x is the age (in years) at which a color TV is replaced. (Round your answer to one decimal place.) yrs (b) What is the probability that someone will keep a color TV more than 5 years before replacement? (Round your answer to four decimal places.) (c) What is the probability that someone will keep a color TV fewer than 10 years before replacement? (Round your answer to four decimal places.) (d) Assume that the average life of a color TV is 9.0 years with a standard deviation of 1.3 years before it breaks. Suppose that a company guarantees color TVs and will replace a TV that breaks while under guarantee with a new one. However, the company does not want to replace more than 11% of the TVs under guarantee. For how long should the guarantee be made (rounded to the nearest tenth of a year)? yrs

Answer #1

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...

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 = 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 = 8.6 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...

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...

How much should a healthy kitten weigh? Suppose that a healthy
10-week-old (domestic) kitten should weigh an average of μ = 26.3
ounces with a (95% of data) range from 14.8 to 37.8 ounces. Let x
be a random variable that represents the weight (in ounces) of a
healthy 10-week-old kitten. Assume that x has a distribution that
is approximately normal. (a) The empirical rule (Section 7.1)
indicates that for a symmetrical and bell-shaped distribution,
approximately 95% of the data...

How much should a healthy kitten weigh? Suppose that a healthy
10-week-old (domestic) kitten should weigh an average of μ = 26.3
ounces with a (95% of data) range from 15.8 to 36.8 ounces. Let x
be a random variable that represents the weight (in ounces) of a
healthy 10-week-old kitten. Assume that x has a distribution that
is approximately normal.
(a) The empirical rule (Section 7.1) indicates that for a
symmetrical and bell-shaped distribution, approximately 95% of the
data...

How much should a healthy kitten weigh? Suppose that a healthy
10-week-old (domestic) kitten should weigh an average of μ
= 25.3 ounces with a (95% of data) range from 15.0 to 35.6 ounces.
Let x be a random variable that represents the weight (in
ounces) of a healthy 10-week-old kitten. Assume that x has
a distribution that is approximately normal.
(a) The empirical rule (Section 7.1) indicates that for a
symmetrical and bell-shaped distribution, approximately 95% of the
data...

How much should a healthy kitten weigh? Suppose that a healthy
10-week-old (domestic) kitten should weigh an average of μ
= 24.7 ounces with a (95% of data) range from 14.6 to 34.8 ounces.
Let x be a random variable that represents the weight (in
ounces) of a healthy 10-week-old kitten. Assume that x has
a distribution that is approximately normal.
(a) The empirical rule (Section 7.1) indicates that for a
symmetrical and bell-shaped distribution, approximately 95% of the
data...

How much should a healthy kitten weigh? Suppose that a healthy
10-week-old (domestic) kitten should weigh an average of μ
= 25.7 ounces with a (95% of data) range from 15.2 to 36.2 ounces.
Let x be a random variable that represents the weight (in
ounces) of a healthy 10-week-old kitten. Assume that x has
a distribution that is approximately normal.
(a) The empirical rule (Section 7.1) indicates that for a
symmetrical and bell-shaped distribution, approximately 95% of the
data...

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