A random variable follows the continuous uniform distribution between 20 and 120.a. Calculate the following probabilities for the distribution.1. P(70≤x≤80)2. P(35 ≤x≤90)3. P(55 ≤x≤ 95)b. What are the mean and standard deviation of this distribution?

Given a random variable (X) follows the continuous uniform distribution between 20 and 120. That is,…

Answered: A random variable follows the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Suppose that the speed at which cars go on the freeway is normally distributed with mean 80 mph and standard deviation 5 miles per hour. Let X be the speed for a randomly selected car. Round all answers to 4 decimal places where possible. 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 76 mph. c. If one of the cars is randomly chosen, find the probability that it is traveling between 82 and 88 mph. d. 86% of all cars travel at least how fast on the freeway? mph. Submit Question
The average student loan debt for college graduates is $25,750. Suppose that that distribution is normal and that the standard deviation is $10,350. Let X = the student loan debt of a randomly selected college graduate. Round all probabilities to 4 decimal places and all dollar answers to the nearest dollar. Find the probability that the college graduate has between $22,700 and $30,000 in student loan debt. (------) The middle 20% of college graduates' loan debt lies between what two numbers? Low: $(______) High: $(_____)
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Logan and Brian began arguing about who did better on their tests, but they couldn't decide who did better given that they took different tests. Logan took a test in Art History and earned a 76.8, and Brian took a test in English and earned a 68.9. Use the fact that all the students' test grades in the Art History class had a mean of 71.9 and a standard deviation of 11.6, and all the students' test grades in English had a mean of 61 and a standard deviation of 9.4 to answer the following questions.a) Calculate the z-score for Logan's test grade.z=z= [Round your answer to two decimal places.] b) Calculate the z-score for Brian's test grade.z=z= [Round your answer to two decimal places.]c) Which person did relatively better? Logan Brian They did equally well.
Suppose that the speed at which cars go on the freeway is normally distributed with mean 66 mph and standard deviation 5 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 62 mph. Round to 4 decumal places. c. If one of the cars is randomly chosen, find the probability that it is traveling between 68 and 71 mph. Round to 4 decimal places.
Let X represent the full height of a certain species of tree. Assume that X has a normal probability distribution with a mean of 58.2 ft and a standard deviation of 4.8 ft. A tree of this type grows in my backyard, and it stands 56.8 feet tall. Find the probability that the height of a randomly selected tree is as tall as mine or shorter. P(X<56.8)= My neighbor also has a tree of this type growing in her backyard, but hers stands 61.1 feet tall. Find the probability that the full height of a randomly selected tree is at least as tall as hers. P(X>61.1)= Enter your answers as decimals accurate to 4 decimal places.
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A random variable follows the continuous uniform distribution between 20 and 120. a. Calculate the following probabilities for the distribution. 1. P(70≤x≤80) 2. P(35 ≤x≤90) 3. P(55 ≤x≤95) b. What are the mean and standard deviation of this distribution?