chapter 3 regen 17 The number of potholes in any given 1mile

chapter 3 regen

17. The number of potholes in any given 1-mile stretch of freeway pavement in Pennsylvania has a Normal distribution. This distribution has a mean of 43 and a standard deviation of 10. Using the Empirical Rule, what is the approximate percentage of 1-mile long roadways with potholes numbering between 23 and 73?

%

18. A company has a policy of retiring company cars; this policy looks at number of miles driven, purpose of trips, style of car and other features. The distribution of the number of months in service for the fleet of cars is Normally distributed with a mean of 44 months and a standard deviation of 9 months. Using the Empirical Rule, what is the approximate percentage of cars that remain in service between 26 and 35 months?

Do not enter the percent symbol.
ans =  %

Solution

Between 0.2 and 0.7, 50% of the population lies

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23<x<73 is equivalent to -2<z<3

prob = 0.4772+0.4987 = 0.9759

i.e. 97.59%

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x between 26 and 35 is equivalent to z between -1 and 1

Hence 68.26%