6. The speeds of vehicles on a highway with posted speed limit 100 km/h are norm

Question

6. The speeds of vehicles on a highway with posted speed limit 100 km/h are normally dis- tributed with mean 112 km/h and standard deviation 8 km/h. Set up integrals to answer the fol- lowing questions, and then use wolframalpha.com, or other computer algebra system (CAS) to compute numerical values. (a) What is the probability that a randomly chosen vehicle is traveling at a legal speed? b) If police are instructed to ticket motorists driving 125 km/h or more, what percentage of motorists are targeted?

Explanation / Answer

a)
mean = 112 , s = 8

p(X <100)

z = (x - mean) / s
= ( 100 - 112) / 8
= 0.25
P(X <100) = P(Z < 0.25) = 0.0668

b)
mean = 112 , s = 8

p(X >125)

z = (x - mean) / s
= ( 125 - 112) / 8
= 1.625
P(X <100) = P(Z <1.625) = 0.0521

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