Answered: The scores of students on the SAT…

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

The scores of students on the SAT college entrance examinations at a certain high school had a normal distribution with mean ?=551 and standard deviation ?=25.9.

(a) What is the probability that a single student randomly chosen from all those taking the test scores 555 or higher?
ANSWER:

For parts (b) through (d), consider a simple random sample (SRS) of 30 students who took the test.

(b) What are the mean and standard deviation of the sample mean score ?¯, of 30 students?
The mean of the sampling distribution for ?¯ is:
The standard deviation of the sampling distribution for ?¯is:

(d) What is the probability that the mean score ?¯ of these students is 555 or higher?
ANSWER:

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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