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Solved: Exercises 39 and 40 refer to the following setting. Ms. Hall gave her class a
Chapter 6, Problem 39(choose chapter or problem)
Exercises 39 and 40 refer to the following setting. Ms. Hall gave her class a 10-question multiple-choice quiz. Let X = the number of questions that a randomly selected student in the class answered correctly. The computer output below gives information about the probability distribution of X. To determine each students grade on the quiz (out of 100), Ms. Hall will multiply his or her number of correct answers by 5 and then add 50. Let G = the grade of a randomly chosen student in the class. N Mean Median StDev Min Max Q1 Q3 30 7.6 8.5 1.32 4 10 8 9 Easy quiz (a) Find the mean of G. Show your method. (b) Find the standard deviation of G. Show your method. (c) How do the variance of X and the variance of G compare? Justify your answer
Questions & Answers
QUESTION:
Exercises 39 and 40 refer to the following setting. Ms. Hall gave her class a 10-question multiple-choice quiz. Let X = the number of questions that a randomly selected student in the class answered correctly. The computer output below gives information about the probability distribution of X. To determine each students grade on the quiz (out of 100), Ms. Hall will multiply his or her number of correct answers by 5 and then add 50. Let G = the grade of a randomly chosen student in the class. N Mean Median StDev Min Max Q1 Q3 30 7.6 8.5 1.32 4 10 8 9 Easy quiz (a) Find the mean of G. Show your method. (b) Find the standard deviation of G. Show your method. (c) How do the variance of X and the variance of G compare? Justify your answer
ANSWER:Problem 39
Exercises 39 and 40 refer to the following setting. Ms. Hall gave her class a 10-question multiple-choice quiz. Let X = the number of questions that a randomly selected student in the class answered correctly. The computer output below gives information about the probability distribution of X. To determine each students grade on the quiz (out of 100), Ms. Hall will multiply his or her number of correct answers by 5 and then add 50. Let G = the grade of a randomly chosen student in the class. N Mean Median StDev Min Max Q1 Q3 30 7.6 8.5 1.32 4 10 8 9 Easy quiz
(a) Find the mean of G. Show your method.
(b) Find the standard deviation of G. Show your method.
(c) How do the variance of X and the variance of G compare? Justify your answer
Step by Step Solution
Step 1 of 3
(a)
Given,
Mean,
We know that the effect on a Random Variable of Multiplying (or Dividing) by a Constant does not change the shape of the distribution. It also multiplies (divides) measures of center and location (mean, median, quartiles, percentiles) by the same constant. And multiplies (divides) measures of spread. Similarly, the effect on a random variable of adding (or Subtracting) a constant adds the constant to (subtracts a from) measures of center and location (mean, median, quartiles, percentiles).
It’s said that Ms. Hall will multiply his or her number of correct answers by 5 and then add 50, to determine each students grade on the quiz (out of 100), ie;
The grade of a randomly chosen student in the class,
Therefore
The mean of G,
