Answered: In May 2018, The College Board reported…

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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In May 2018, The College Board reported the following mean scores for two parts of the Scholastic Aptitude Test (SAT):

Evidenced-Based Reading and Writing 533

Mathematics 527

Assume the population standard deviation on each part of the test is σ = 100.

a. What is the probability a sample of 90 test-takers will provide a sample mean test score within 10 points of the population mean of 533 on the Evidence-Based Reading and Writing part of the test?

b. What is the probability a sample of 90 test-takers will provide a sample mean test score within 10points of the population mean of 527 on the Mathematics part of the test?

c. Comment on the differences between the values computed in parts (a) and (b)?

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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