Answered: Changing the mean and standard…

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

Changing the mean and standard deviation of a Normal distribution by a moderate amount can greatly change the percent of observations in the tails. Suppose a college is looking for applicants with either SAT Math or Evidence-Based Reading and Writing (ERW) scores 770 and above.

(a) In 2018, the scores of men on the math SAT followed the N(526,120) distribution. What percent of men scored 770 or better? Round your answer to two decimal places.

percent:

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

$g i v e n d a t a, n o r m a l d i s t r i b u t i o n i n 2018 t h e s c o r e s o f m e n o n t h e m a t h S A T f o l l o w s t h e X ~ N (526, 120) d i s t r i b u t i o n h e r e μ = 526 σ = 120$