Exercise : Interstates driving speeds in the US have an average of 70 mph with a

Question

Exercise : Interstates driving speeds in the US have an average of 70 mph with a standard deviation of 10 mph. (a) Suppose these driving speeds follow a mounded bell shaped distribution. a. What percentage of drivers in the US drive between 50 mph and 80 mph? b. If driving above 80 mph in the US will result in a speeding ticket, what percent of drivers will end up with a speeding ticket? vc. Let thefollowing represent asample ofdrivers' speedst 67 3555 572 3 75 74 6,83 81,78 67 so with corresponding sample mean and sample standard deviation are 7.69 and 12.6, respectively. Find d. Using the 1.5 x IQR rule, determine if there exists any outlier(s) in the sample. Using the empirical (b) Now suppose the distribution of interstates driving speeds-in-the US is unknown but with the same the five numbers summary of this sample and provide the interpretation of the third quartile. rule, determine if there exists any outlier(s) in the sample. characteristics (mean 70 mph and standard deviation 10 mph). Using Chebyshev's rule, at most what percent of drivers in the US drive less than 40 mph or more than 100 mph?

Explanation / Answer

d)

by empirical rule if

X > mean +3 *sd , or < mean - 3 *sd

> 70 + 3*10 or < 70 - 3*10

> 100 or < 40

there is only one outlier 35 by empirical rule

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