Question: Consumer Reports gave information about the ages at which various household products are replaced. For example, color TVs are replaced at an average age of
(a) The empirical rule (Section 7.1) indicates that for a symmetrical 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 ˆ’ 2σ to μ + 2σ is often used for €œcommonly occurring€ data values. The interval from μ ˆ’ 2σ to μ + 2σ is 4σ in length. This leads to a €œrule of thumb€ for estimating the standard deviation from a 95% range of data values.
Estimating the standard deviation
For a symmetrical, bell-shaped distribution,
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where it is estimated that about 95% of the commonly occurring data values fall into this range.
Use this €œrule of thumb€ to approximate the standard deviation of x values, where x is the age (in years) at which a color TV is replaced.
(b) What is the probability that someone will keep a color TV more than 5 years before replacement?
c) What is the probability that someone will keep a color TV fewer than 10 years before replacement?
(d) Assume that the average life of a color TV is 8 years with a standard deviation of 1.5 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 10% of the TVs under guarantee. For how long should the guarantee be made (rounded to the nearest tenth of a year)?
range high value low value standard deviation 4. 4
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