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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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