n.net/web/Student/Assignment-Responses/submitidep-16128082 of data) range was fr
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n.net/web/Student/Assignment-Responses/submitidep-16128082 of data) range was from 4.s to 9.6 years. Thus, the range was 9.6-4 Suppose, household color TVs are replaced at an average age of, 72 years after purchase, and the Cot-of datal range was lrem -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 symmetrical and bell shaped dstribution, approximately 95% of the data les within two standard deviations of the mean. Therefore, a 99% range of data values extending from . 20 to + 20 is often used for-commonly occurring, data values. Note that the interval from ·20to +2o is 4s in length. This leads to a "rule of thumb" for estimating the standar d deviation from a 9% range of data va Estimating the standard deviation For a symmetric, bell shaped distribution, rane standard deviation high value-low value 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 place.) deviation of x valuses, where x is the age (in years) at which a color TV is raplaced. (Round your and (in years) at which a coler TV is replaced. (Round your answer to one decimal yrs (b) What is the probability that someone will keap a color TV more than 5 years before replacem ent? (Round your answer to four decimal places.) c) what is the probability that someone will keep a color TV fewer than 10 years before fewer than 10 years before replacement? (Round your answer to four decimal places.) average life of a color TV is 7.2 years with a standard deviation of 1.2 years before it breaks. Suppose (d) Assume that the average life of a color TV is 7 2 years with standard deviation of i replace a TV that breaks while under guarantee with a new one,However, the should the guarantee be made (rounded to the nearest tenth of a year)? and will re it breaks. Suppose that a company quarantees color Tvs does not want to replace more than 14% of the TVs under guarantee, nor how long nen one. However, the company yrs Noed Holp Type here to searchExplanation / Answer
a. According to rule of thumb, the standard deviation of x values, where, x is age (in years) is as follows:
Standard deviation=range/4=(9.6-4.8)/4=1.2 years.
b. The probability that someone will keep a color TV more tahn 5 yeras before replacement is as follows:
P(x>5)=1-P(x<=5)=1-P[Z<=(5-7.2)/1.2] (use, the Z score formula, Z=(x-mu)/sigma, where, x is raw data, mu i spopulation mean, and sigma is population standard deviation).
=1-P(Z<=-1.83)
=1-0.0336 [look into Z table, the table gives area under standard normal curve to the left of Z]
=0.9664 (ans)
c. P(x<10)=P(x<=9)=P[Z<=(9-7.2)/1.2]
=P[Z<=1.5]
=0.9332 (ans)
d. From information given, P(X<=x)=0.86 [company wants to replace 86% of the TVs unedr gurantee]. Find closest Z score corresponding to the area 0.86 from Z table. The area is 0.8599, and the corresponding Z score is 1.08. Unstandardize the value by substituting the Z score in the follow ing formula.
Age=mean+Zscore*standard deviation
=7.2+1.08*1.2
= 8.496
=8.5 years (ans)
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