A set of final examination grades in an introductory statistics course is normally dis-tributed with a mean of 77 and a standard deviation of 11.(a) What is the probability of an individual student getting a grade above 95 on thisexam?(b) What is the probability of an individual student getting a grade below 69 on thisexam?(c) What is the probability of an individual student getting a grade between 84 and 92on this exam?(d) Explain mathematically what was different in the solving process for each of theabove three problems.

Answered: A set of final examination grades in an…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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A set of final examination grades in an introductory statistics course is normally dis-
tributed with a mean of 77 and a standard deviation of 11.
(a) What is the probability of an individual student getting a grade above 95 on this
exam?
(b) What is the probability of an individual student getting a grade below 69 on this
exam?
(c) What is the probability of an individual student getting a grade between 84 and 92
on this exam?
(d) Explain mathematically what was different in the solving process for each of the
above three problems.

Expert Solution

Step 1

Hey, since there are multiple subparts posted, we will answer first three subparts. If you want any specific subpart to be answered then please submit that subpart only or specify the subpart in your message.

Given:

$\begin{array}{rcl} μ & = & 77 \\ σ & = & 11 \end{array}$

a) The probability of an individual student getting a grade above 95 on this exam is obtained as below:

$\begin{array}{rcl} P (X > 95) & = & P (\frac{X - μ}{σ} > \frac{95 - 77}{11}) \\ = & P (Z > 1.6364) \\ = & 1 - P (Z < 1.6364) \end{array}$

The p-value is obtained from Excel using "=NORMSDIST(z)".

Output obtained using Excel is given below:

From the output, the P(Z<1.6364) is 0.9491.

$\begin{array}{rcl} P (X > 95) & = & 1 - 0.9491 \\ = & 0.0509 \end{array}$

Thus, the probability of an individual student getting a grade above 95 on this exam is 0.0509.

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