
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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![**Educational Text: Probability and Normal Distribution of Car Speeds**
*Contextual Scenario:*
Suppose that the speed at which cars go on the freeway is normally distributed with a mean of 78 mph and a standard deviation of 9 miles per hour. Let \( X \) be the speed for a randomly selected car.
**Questions:**
a. What is the distribution of \( X \)?
- \( X \sim N(\mu, \sigma^2) \)
b. If one car is randomly chosen, find the probability that it is traveling more than 75 mph. Round to 4 decimal places.
- [Input box for answer]
c. If one of the cars is randomly chosen, find the probability that it is traveling between 81 and 87 mph. Round to 4 decimal places.
- [Input box for answer]
*Notes on Application:*
- When addressing parts b and c, the calculations will involve determining z-scores and using the standard normal distribution table to find probabilities related to specific speed ranges.
*For Educational Purpose:*
This exercise helps in understanding the application of normal distribution in real-world scenarios such as analyzing vehicle speeds on a freeway. It aids in comprehending statistical concepts like mean, standard deviation, and probability using the normal distribution model.](https://content.bartleby.com/qna-images/question/0f725b05-6985-474e-a031-937034e54c0f/d2c6bf3e-b479-4df7-9686-84b0c1e0014d/45yxd9x_thumbnail.jpeg)
Transcribed Image Text:**Educational Text: Probability and Normal Distribution of Car Speeds**
*Contextual Scenario:*
Suppose that the speed at which cars go on the freeway is normally distributed with a mean of 78 mph and a standard deviation of 9 miles per hour. Let \( X \) be the speed for a randomly selected car.
**Questions:**
a. What is the distribution of \( X \)?
- \( X \sim N(\mu, \sigma^2) \)
b. If one car is randomly chosen, find the probability that it is traveling more than 75 mph. Round to 4 decimal places.
- [Input box for answer]
c. If one of the cars is randomly chosen, find the probability that it is traveling between 81 and 87 mph. Round to 4 decimal places.
- [Input box for answer]
*Notes on Application:*
- When addressing parts b and c, the calculations will involve determining z-scores and using the standard normal distribution table to find probabilities related to specific speed ranges.
*For Educational Purpose:*
This exercise helps in understanding the application of normal distribution in real-world scenarios such as analyzing vehicle speeds on a freeway. It aids in comprehending statistical concepts like mean, standard deviation, and probability using the normal distribution model.
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- Cal Poly Pomona found that 15% of its students withdraw without completing Calculus I course. Assume that 30 students registered for the course. Let X be the number of students who withdraw. What distribution does X follow?arrow_forwardSuppose that the speed at which cars go on the freeway is normally distributed with mean 78 mph and standard deviation 6 miles per hour. Let X be the speed for a randomly selected car. Round all answers to 4 decimal places where possible. b. If one car is randomly chosen, find the probability that it is traveling more than 76 mph. __________c. If one of the cars is randomly chosen, find the probability that it is traveling between 77 and 80 mph. ___________d. 60% of all cars travel at least how fast on the freeway?_____________ mph.arrow_forwardPlease answer B, C, & D.arrow_forward
- Subpart A,B,Carrow_forwardYou have a uniform distribution whose lowest value is 7 and whose highest value is 15. Find the probability that a randomly selected number from this distribution will be between 9.3 and 10.6.arrow_forwardThe NJ Department of Health has reported the average life span of NJ residents is 81 years. If the standard deviation is σ = 4 years, what is the probability of a person living to at least 92 years of age?arrow_forward
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