Suppose that the speed at which cars go on the freeway is normally distributed with mean 78 mph and standard deviation 9 miles per hour. Let X be the speed for a randomly selected car. a. What is the distribution of X? X - N( b. If one car is randomly chosen, find the probability that it is traveling more than 75 mph. Round to 4 decumal places. 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.
Suppose that the speed at which cars go on the freeway is normally distributed with mean 78 mph and standard deviation 9 miles per hour. Let X be the speed for a randomly selected car. a. What is the distribution of X? X - N( b. If one car is randomly chosen, find the probability that it is traveling more than 75 mph. Round to 4 decumal places. 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.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0f725b05-6985-474e-a031-937034e54c0f%2Fd2c6bf3e-b479-4df7-9686-84b0c1e0014d%2F45yxd9x_processed.jpeg&w=3840&q=75)
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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