Answered: For each problem, sketch 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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Question

For each problem, sketch the distribution and shade in the area that represents the answer to the question.

A continuous random variable X has a uniform distribution where X can take on any value between 8 and 20. What is the probability that X is greater than 12?
A random variable Y has normal distribution with a mean of 80 and a standard deviation of 15. What value of Y cuts off the top ten percent of the values for Y?

For questions 3 - 5, use the following information: Soda is often packaged in cans that are supposed to contain 12 ounces. However, no manufacturing plant is perfect and so there might be slight errors. For example, Sam's Splendid Soda company has verified that the amount of soda in their cans has a normal distribution with a mean of 12 ounces and a standard deviation of 0.75 ounces. Although this is made up, it's not completely divorced from the truth.

You open a can of Sam's and realize there are only 11.6 oz in the can. What is the probability that a single can will contain 11.6 ounces or less of soda?
Troubled by the under-filled soda, you decide to empty out all the cans in a six pack of Sam's Soda and find that the mean amount of soda in all the cans is 11.6 ounces. What is the probability that six pack will have a mean of 11.6 ounces or less of soda?
Not satisfied with the information you figured out in #2, you take a case (36 cans) and empty out all the cans of Sam's Soda and find that the mean amount of soda in all the cans is 11.6 ounces. What is the probability that case will have a mean of 11.6 ounces or less of soda?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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