Answered: Find the following probabilities. It…

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

Find the following probabilities. It may help to sketch the pdf for Standard Normal Distribution
and shade in the area that corresponds to the probability of interest.
1) Z ~ Norm(0, 1), find Pr(Z ≤ 1.78)
2) Z ~ Norm(0, 1), find Pr(Z > 1.96)
3) Z ~ Norm(0, 1), find Pr(-2.34 ≤ Z < 1.45)
4) Z ~ Norm(0, 1), find Pr(Z < -0.67)
5) Z ~ Norm(0, 1), find Pr(Z = 2.3)
6) Z ~ Norm(0, 1), find Pr(Z ≥ -2.98)

Do the same for the following below. Note however that they are no longer Standard Normal
Distributions.
7) X ~ Norm(266, 16^2), find Pr(X < 200)
8) X ~ Norm(-2, 5^2), find Pr(-4 < X < -3)
9) X ~ Norm(-2, 5^2), find Pr(X = -3)
10) X ~ Norm(64.4, 2.4^2), find Pr(|X| > 70)

Definition Definition Probability of occurrence of a continuous random variable within a specified range. When the value of a random variable, Y, is evaluated at a point Y=y, then the probability distribution function gives the probability that Y will take a value less than or equal to y. The probability distribution function formula for random Variable Y following the normal distribution is: F(y) = P (Y ≤ y) The value of probability distribution function for random variable lies between 0 and 1.

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