Suppose, household color TVs are replaced at an average age of μ = 8.4 years after purchase, and the (95% of data) range was from 6.4 to 10.4 years. Thus, the range was 10.4 − 6.4 = 4.0 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 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. 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 8.4 years with a standard deviation of 1.0 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 9% of the TVs under guarantee. For how long should the guarantee be made (rounded to the nearest tenth of a year)? yrs

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Suppose, household color TVs are replaced at an average age of μ = 8.4 years after purchase, and the (95% of data) range was from 6.4 to 10.4 years. Thus, the range was 10.4 − 6.4 = 4.0 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 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.

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 8.4 years with a standard deviation of 1.0 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 9% of the TVs under guarantee. For how long should the guarantee be made (rounded to the nearest tenth of a year)?
yrs

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