Answered: Suppose xx is a normally distributed…

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

Suppose xx is a normally distributed random variable with μ=8.9μ=8.9 and σ=3.9σ=3.9. Find each of the following probabilities:

(a) P(6.8≤x≤16.2)=P(6.8≤x≤16.2)=

(b) P(8.6≤x≤14.7)=P(8.6≤x≤14.7)=

(d) P(x≥6.3)=P(x≥6.3)=

(e) P(x≤16.4)=P(x≤16.4)=

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.

Expert Solution

Step 1

As per our guidelines we are supposed to answer only 3 sub-parts of any questions so i am solving first 3 sub-parts only please post the other part separately to get answer

We have given that

Mean(µ) = 8.9
Standard deviations (σ) = 3.9
X ~ N (µ, σ )= N(8.9, 3.9)