Suppose the distribution of speeds of cars traveling on the I-5 in California is nearly normal with a mean of 72.6 miles/hour and a standard deviation of 4.78 miles/hour. The speed limit on a stretch of the I-5 is 70 miles/hour.(a) What percentage of cars travel above the speed limit?(b) A highway patrol officer is hidden one the side of the freeway. What is the probability that 5 cars pass and none are speeding? Assume that the speeds of cars are independent of each other.(c) On average, how many cars would the highway patrol officer expect to watch until the first car that is speeding?

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Asked Oct 31, 2019
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Suppose the distribution of speeds of cars traveling on the I-5 in California is nearly normal with a mean of 72.6 miles/hour and a standard deviation of 4.78 miles/hour. The speed limit on a stretch of the I-5 is 70 miles/hour.

(a) What percentage of cars travel above the speed limit?

(b) A highway patrol officer is hidden one the side of the freeway. What is the probability that 5 cars pass and none are speeding? Assume that the speeds of cars are independent of each other.

(c) On average, how many cars would the highway patrol officer expect to watch until the first car that is speeding?

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Expert Answer

Step 1

Solution:

a.The percentage of cars travel above the speed limit is obtained below:

Let the random variable X be the speeds of cars traveling on the I-5 in California follows normal distribution with population mean speed as 72.6 miles/ hour and standard deviation score as 4.78 miles/hour. The speed limit on a stretch of the I-5 is 70 miles/hour.

The percentage of cars travel above the speed limit is 0.7068.

From Excel, 1-NORM.DIST(70,72.6,4.78,TRUE)=0.7068

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f 1-NORM.DIST(70,72.6,4.78, TRUE) A1 B c D E F G 1 0.7068

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Step 2

b.The probability that 5 cars pass and none are speeding is obtained below:

Let A be the even that speeding.

P(AC)=1-P(...

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P()x P()xP(4f)x] P(4°)x P( °) -P() -[0.2932 5 cars pass and none are speeding, 0.0022

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