Answered: There are two college entrance exams…

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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There are two college entrance exams that are often taken by students, the ACT and the SAT. The composite score on the ACT is approximately normally distributed with mean 21.1 and standard deviation 5.1.
The composite score on the SAT is approximately normally distributed with mean 1026 and standard deviation 210. Suppose you scored 28 on the ACT and 1182 on the SAT. Which exam did you score better on? Justify your reasoning using the normal model.

Choose the correct answer below.

A. The score on the ACT

is better, because the percentile for the

the ACT

score is higher.

The score on the ACT is better, because the difference between the score and the mean is lower than it is for the SAT.

The score on the SAT is better, because the score is higher than the score for the ACT.

The score on

the SAT

is better, because the percentile for the

the SAT

score is higher.

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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