Consumer Reports gave information about the ages at which various household products are replaced. For example, color
Question:
(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)?
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Age at replacement x is approximately normal with 8 and rang...View the full answer
