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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 (μ)=$0.50
Population standard deviation (σ)=$15.80
Let's estimate the value of the mean and standard deviation of the total payoff:
μX+X=μX+μX=0.50+0.50=$1

Then,

σX+X=σX2+σX2=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:

μX+X−2=μX+μX−2=2(0.50)−2=−$1

Then,

σX+X−2=σX2+σX2=15.802+15.802=22.34

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Most popular questions from this chapter

Most states and Canadian provinces have government-sponsored lotteries. Here is a simple lottery wager, from the Tri-State Pick 3game that New Hampshire shares with Maine and Vermont. You choose a number with 3digits from 0to 9; the state chooses a three-digit winning number at random and pays you \(500if your number is chosen. Because there are 1000numbers with three digits, you have a probability of 1/1000of winning. Taking Xto be the amount your ticket pays you, the probability distribution of Xis

(a) Show that the mean and standard deviation of Xare μX=\)0.50and σX=\(15.80.

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Running a mile A study of 12,000able-bodied male students at the University of Illinois found that their times for the mile run were approximately Normal with mean 7.11minutes and standard deviation 0.74 minute. Choose a student at random from this group and call his time for the mile Y. Find P(Y<6) and interpret the result. Follow the four-step process.
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