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
bellshaped 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, bellshaped distribution,
standard deviation ≈ 

≈ 

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 7.8 years with a
standard deviation of 1.2 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 13% of the TVs under guarantee. For how
long should the guarantee be made (rounded to the nearest tenth of
a year)?
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