Answered: The scores on the Accuplacer test and…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

The scores on the Accuplacer test and High School GPAs are normally distributed.
The Accuplacer test had a mean of 35 and a standard deviation of 8.
High School GPAs had a mean of 2.6 and a standard deviation of 0.2.
What high school GPA do you need to equal a score of 26 on the Accuplacer test?
Give answer to two decimal places.

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 + ...

Expert Solution

Step 1: Given Information

The mean of the Accuplacer test, $mu subscript A equals 35$

The standard deviation of the Accuplacer test, $sigma subscript A equals 8$

The mean of the High School GPAs, $mu equals 2.6$

The standard deviation of the High School GPAs, $sigma equals 0.2$

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