Answered: A history professor is making up a…

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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A history professor is making up a final examination
that is to be given to a very large group of students. His
feelings about the average grade that they should get is
expressed subjectively by a normal distribution with the
mean μ0 = 65.2 and the standard deviation σ0 = 1.5.
(a) What prior probability does the professor assign to
the actual average grade being somewhere on the interval
from 63.0 to 68.0?
(b) What posterior probability would he assign to this
event if the examination is tried on a random sample of 40
students whose grades have a mean of 72.9 and a standard
deviation of 7.4? Use s = 7.4 as an estimate of σ.

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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