Question

4.38 Speeding on the I-5, Part II. Exercise 4.36 states that the distribution of speeds of cars traveling on the Interstate 5 Freeway (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 this stretch of the I-5 is 70 miles/hour. (a) A highway patrol officer is hidden on the side of the freeway. What is the probability that 5 cars pass and none are speeding? Assume that the speeds of the cars are independent of each other. (b) On average, how many cars would the highway patrol officer expect to watch until the first car that is speeding? What is the standard deviation of the number of cars he would expect to watch?

          4.38 Speeding on the I-5, Part II. Exercise 4.36 states that the distribution of speeds of cars traveling on
the Interstate 5 Freeway (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 this stretch of the I-5 is 70 miles/hour.
(a) A highway patrol officer is hidden on the side of the freeway. What is the probability that 5 cars pass
and none are speeding? Assume that the speeds of the cars are independent of each other.
(b) On average, how many cars would the highway patrol officer expect to watch until the first car that is
speeding? What is the standard deviation of the number of cars he would expect to watch?

Show more…

4.38 Speeding on the I-5, Part II. Exercise 4.36 states that the distribution of speeds of cars traveling on
the Interstate 5 Freeway (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 this stretch of the I-5 is 70 miles/hour.
(a) A highway patrol officer is hidden on the side of the freeway. What is the probability that 5 cars pass
and none are speeding? Assume that the speeds of the cars are independent of each other.
(b) On average, how many cars would the highway patrol officer expect to watch until the first car that is
speeding? What is the standard deviation of the number of cars he would expect to watch?

Added by Manuela E.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Supreeta N

03/07/2023

Step 1

(a) Show more…

Show all steps

lock

Thanks for your feedback!

Play audio

Feedback

Powered by NumerAI

Supreeta N and 60 other subject Intro Stats / AP Statistics educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Recommended Videos

Recommended Textbooks

Transcript

00:02 Hello students, according to the given question, we have to find out the probability values.

00:08 So given the mean value that is mu is 72 .6 miles per hour and standard deviation sigma is equal to 4 .78.

00:22 And they have given speed limit on the strength of 1 to 5 is 70 million miles per hour.

00:35 So now the probability of car speed that is x greater than 70 will be equal to probability of x greater than 70.

00:46 That is equal to 1 minus probability of x less than or equal to 70, which is equal to 1 minus probability of x less than or equal to 70, which is equal to to 1 minus probability of z less than or equal to 70 minus mu that is 72 .6 is divided by sigma that is 4 .78.

01:06 So which is equal to 1 minus probability of z less than minus 0 .5439.

01:14 So from the z table we get the value that is 1 minus 0 .2933.

01:22 So which is equal to 0 .7067.

01:27 So in the a bit we have to find probability that 5 cars, pass and none are speeding.

01:45 So which is equal to the value we got the probability that is 1 minus 0 .7067 whole power 5 cars.

01:56 So power 5 so which is equal to 0 .00217.

02:03 In the b bit we have to find here standard deviation.

02:08 So here the number of cars would the highway patrol highway patrol officer expect to watch watch until the first car that is speeding.

02:38 So that is equal to r by p...

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later