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Chapter 6: Q. 53 (page 380)

53. The Tri - State Pick 3Refer to Exercise 42. Suppose you buy a $1 ticket on each of two different days.
(a) Find the mean and standard deviation of the total payoff. Show your work.
(b) Find the mean and standard deviation of your total winnings. Interpret each of these values in context.

Short Answer

Expert verified

(a) The mean and standard deviation of the total payoff are $1.00and $22.34.

(b) The mean and standard deviation of your total winnings are -$1.00and $22.34.

Step by step solution

01

Part (a) Step 1: Given information

We have to refer the exercise 42 and find the mean and standard deviation of the total payoff.

02

Part (a) Step 2: Calculate the mean and standard deviation of total payoff

According to the information, the population mean (渭)=$0.50
Population standard deviation (蟽)=$15.80
Let's estimate the value of the mean and standard deviation of the total payoff:
渭X+X=渭X+渭X=0.50+0.50=$1

Then,

蟽X+X=蟽X2+蟽X2=15.802+15.802=22.34

03

Part (b) Step 1: Given information

Refer the exercise 42. We have to find the mean and standard deviation of the total winnings.

04

Part (b) Step 2: Calculate the mean and standard deviation of total winnings

Let's consider the total payoff isX.
Hence, P=X+X-2=2X-2

Now find the mean and standard deviation of the total payoff as:

渭X+X鈭�2=渭X+渭X鈭�2=2(0.50)鈭�2=鈭�$1

Then,

蟽X+X鈭�2=蟽X2+蟽X2=15.802+15.802=22.34

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Most popular questions from this chapter

52. Study habits The academic motivation and study habits of female students as a group are better than those of males. The Survey of Study Habits and Attitudes (SSHA)is a psychological test that measures these factors. The distribution of SSHAscores among the women at a college has mean120and standard deviation 28, and the distribution of scores among male students has mean 105and standard deviation 35.You select a single male student and a single female student at random and give them theSSHA test.
(a) Explain why it is reasonable to assume that the scores of the two students are independent.
(b) What are the expected value and standard deviation of the difference (female minus male) between their scores?
(c) From the information given, can you find the probability that the woman chosen scores higher than the man? If so, find this probability. If not,
explain why you cannot.

54. The Tri -State Pick 3Refer to Exercise 42. Suppose 365
(a) Find the mean and standard deviation of your total winnings. Show your work.
(b) Interpret each of the values from (a) in context .

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 student鈥檚 grade on the quiz (out of localid="1649489099543" 100), Ms. Hall will multiply his or her number of correct answers by 10. Let localid="1649489106434" G=the grade of a randomly chosen student in the class.

localid="1649489113566" NMeanMedianStDevMinMaxQ1Q3307.68.51.3241089

(a) Find the mean of localid="1649489121120" G. Show your method.

(b) Find the standard deviation of localid="1649489127059" G. Show your method.

(c) How do the variance of localid="1649489132289" Xand the variance oflocalid="1649489138146" Gcompare? Justify your answer.

Suppose you roll a pair of fair, six-sided dice until you get doubles. Let T=the number of rolls it takes.

In the game of Monopoly, a player can get out of jail free by rolling doubles within 3turns. Find the probability that this happens

A report of the National Center for Health Statistics says that the height of a 20-year-old man chosen at random is a random variable H with mean 5.8feet (ft) and standard deviation0.24 ft. Find the mean and standard deviation of the height J of a randomly selected 20-year-old man in inches. There are 12 inches in a foot
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