The average annual mileage of a car is 23,500 kilometers, with a standard deviation of 3900 kilometers, according to a sample of 100 Virginians who own cars.Assume that the measurement distribution is roughly normal.a) Create a 99 percent confidence interval for the typical Virginian vehicle's annual mileage in kilometers.b) If we assume that Virginians drive an average of 23,500 kilometers per year, what can we say with 99 percent certainty about the potential extent of our error?

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The average annual mileage of a car is 23,500 kilometers, with a standard deviation of 3900 kilometers, according to a sample of 100 Virginians who own cars.Assume that the measurement distribution is roughly normal.a) Create a 99 percent confidence interval for the typical Virginian vehicle&#039;s annual mileage in kilometers.b) If we assume that Virginians drive an average of 23,500 kilometers per year, what can we say with 99 percent certainty about the potential extent of our error?

Ian Adams · Accepted Answer

a) The 99% confidence interval for the average number of kilometres an automobile is driven is obtained below: The value of mean is 23,500 kilometres, population standard deviation is 3,900 and sample size (n)=100 Critical value: From the standard normal distribution table, for the 99% confidence level the critical values is (z⋅)2.58. The confidence interval formula for the population mean is, C.I.=x―±z⋅σn Substitute mean =23,500, standard deviation (σ) is 3,900 and sample size (n)=100. C.I.=x―±z⋅σn =23,500±2.583.900100 =23,500±2.58(390) =23,500±1006.2 =(23,500−1006.2, 23,500+1006.2) =(22,493.8, 24,506.2) Thus, the 99% confidence interval for the average number of kilometres an automobile is between 22,493.8 and 24,506.2. b) The required formula is obtained below: ME=zα2(σn) Substitute 3,900 for σ, 100 for n and 2.58 for Zα2. ME=2.58(3,900100) =2.58(3,90010) =2.58(390) =1006.2 With 99% confidence that the possible size of our error will not exceed the 1006.2 kilometres.

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