MATLAB: An Introduction with Applications
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.
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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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