Example 2: For each part below, find the endpoints on a standard normal density (curves have X~N(0,1) ). The area to the left of the endpoint is about 0.20.The area between ± z is 0.80.The area to the right of the endpoint is 0.4

Suppose, X is Normally distributed with mean 0 and variance 1. The probability density function of X is fx=12πe-12x2, x∈ℝ1. Suppose, the endpoint is z The area to the left of the z is P[X≤z]. Given that, the area to the left of the endpoint is 0.20. P[X≤z]=0.20. From the normal distribution table, P[X≤-0.8416]=0.20. Therefore, the endpoint is z=-0.8416. 2. The area between ± z is P-z≤X≤z=PX≤z-PX<-z=PX≤z-PX> z, X=D-X=PX≤z-1+PX≤z=2PX≤z-1 Given that, The area between ± z is 0.80. P-z≤X≤z=0.80⇒2PX≤z-1=0.80⇒PX≤z=0.90 From the normal distribution table, P[X≤1.2816]=0.90. Therefore, the endpoint is z=1.2816.3. Suppose, The endpoint is z. The area to the right of the endpoint z is P[X>z]=1-PX≤z Given that, the area to the right of the endpoint is 0.40. P[X>z]=0.40⇒1-PX≤z=0.40⇒PX≤z=0.60 From the normal distribution table, P[X≤0.2533]=0.60. Therefore, the endpoint is z=0.2533.

Answered: Example 2: For each part below, find…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Concept explainers

Question

Example 2: For each part below, find the endpoints on a standard normal density (curves have X~N(0,1) ).

The area to the left of the endpoint is about 0.20.
The area between ± z is 0.80.
The area to the right of the endpoint is 0.4

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Point Estimation, Limit Theorems, Approximations, and Bounds$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions