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A construction zone on a highway has a posted speed limit of 40 miles per hour....

A construction zone on a highway has a posted speed limit of 40 miles per hour. The speeds of vehicles passing through this construction zone are normally distributed with a mean of 45 miles per hour and a standard deviation of 5.6 miles per hour. Find the percentage of vehicles passing through this construction zone that are exceeding the posted speed limit. Round to four decimal places.

Math   Statistics-And-Probability   
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Answer #1

X: speed of vehicle passing through this construction zone

X follows normal distribution with mean of 45 miles per hour and a standard deviation of 5.6 miles per hour

Speed limit : 40 miles per hour.

Probability of a vehicle passing through this construction zone that are exceeding the posted speed limit : P(X>40)

P(X>40) = 1- P(X40)

P(X40)

Z-score for 40 = (40-mean)/Standard deviation = (40-45)/5.6 = -5/5.6 = - 0.89

From standard normal table, P(Z-0.89) = 0.1867

P(X40) = P(Z-0.89) = 0.1867

P(X>40) = 1- P(X40) = 1 - 0.1867 = 0.8133

Probability of a vehicle passing through this construction zone that are exceeding the posted speed limit : P(X>40) = 0.8133

Percentage of vehicles passing through this construction zone that are exceeding the posted speed limit = 0.8133 x 100 = 81.33%

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