Answered: Let the random variable X represent…

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

Let the random variable X represent test 1 scores of the students who take a math class. Suppose that X follows a normal distribution with mean 60 and standard deviation 15.

1) When student A gets 70 from test 1 what would be his z-score and if the score of student B corresponds to the z-score z= -1.4, what is his original score?

2) Find the R code which can be used to calculate the probability that one student's score fall between 75 and 90.

Options for 2)

a) pnorm(90) - pnorm(75)

b) pnorm(90, 15, 60) - pnorm(75, 15, 60)

c) pnorm(2, 60, 15) - pnorm(1, 60, 15)

d) pnorm(2) - pnorm(1)

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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