Question

Suppose the average score on a national test is 500 with a standard deviation of 100 . If each score is increased by $25 \%,$ what are the new mean and standard deviation, respectively? (A) 500 and 100 (B) 525 and 100 (C) 625 and 100 (D) 625 and 105 (E) 625 and 125

Name: Problem 5, Chapter 1: AP Statistics with 6 Practice Tests
Uploaded: 2023-09-11T08:57:05-08:00
Channel: Tanvi Garg
Description: Suppose the average score on a national test is 500 with a standard deviation of 100 . If each score is increased by 25 %, what are the new mean and standard deviation, respectively? (A) 500 and 100 (B) 525 and 100 (C) 625 and 100 (D) 625 and 105 (E) 625 and 125

   Suppose the average score on a national test is 500 with a standard deviation of 100 . If each score is increased by $25 \%,$ what are the new mean and standard deviation, respectively?
(A) 500 and 100
(B) 525 and 100
(C) 625 and 100
(D) 625 and 105
(E) 625 and 125

AP Statistics with 6 Practice Tests

Martin Sternstein 11th Edition

Chapter 1, Problem 5

Instant Answer

Solved by Expert Tanvi Garg

09/11/2023

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Step 1: We are given that the average score on a national test is 500 with a standard deviation of 100. Show more…

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Suppose the average score on a national test is 500 with a standard deviation of 100 . If each score is increased by $25 \%,$ what are the new mean and standard deviation, respectively? (A) 500 and 100 (B) 525 and 100 (C) 625 and 100 (D) 625 and 105 (E) 625 and 125

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Key Concepts

Linear Transformation of Random Variables

This concept involves modifying a random variable by applying a mathematical function, typically of the form Y = aX + b. When a random variable is multiplied by a constant (a) and/or has a constant added to it (b), its statistical properties change in predictable ways. Specifically, the mean becomes a times the original mean plus b, and the standard deviation becomes the absolute value of a times the original standard deviation.

Effect of Scaling on Mean and Standard Deviation

When every score in a data set is multiplied by a constant factor, the mean is multiplied by that same factor and the standard deviation is also multiplied by the absolute value of that factor. In this question, a 25% increase means multiplying each test score by 1.25, resulting in new values for the mean and standard deviation.

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