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Chapter 6: Q. 54 (page 380)

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 .

Short Answer

Expert verified

(a) The mean and standard deviation of your total winnings are -$182.50and $301.86.

(b) The standard deviation shows that there will be loss of $182.50 in an year which may average on an average by $5767 in a year.

Step by step solution

01

Part (a) Step 1: Given information

Given in the question that the mean and standard deviation of the total winnings.

02

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

According to the information, the population mean:

(μ)=$0.50
Population standard deviation:

(σ)=$15.80.

Let's determine the mean and standard deviation of the total payoff as:

localid="1649873876116" μP=365μX−365=365(0.50)+0.50=−$182.50

Then,
localid="1649873879625" σp=σX12+σX22+…+σX3652=365(15.80)=$301.86

03

Part (b) Step 1: Given information

Interpret the values that determined from (a) in context.

04

Part (b) Step 2: Interpret the values

Let's consider the result from part (a):
μ=−$182.50

σ=$5767.00

Hence, will lose about $182.50in a year on average, which will vary on average by about $5767.00in a year.

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Most popular questions from this chapter

A large auto dealership keeps track of sales and leases agreements made during each hour of the day. Let X= the number of cars sold and Y= the number of cars leased during the first hour of business on a randomly selected Friday. Based on previous records, the probability distributions of Xand Yare as follows:

Define D=X-Y.

The dealership’s manager receives a 500bonus for each car sold and a300 bonus for each car leased. Find the mean and standard deviation of the difference in the manager’s bonus for cars sold and leased. Show your work.

50. Checking independence For each of the following situations, would you expect the random variables Xand Yto be independent? Explain your answers.

(a)Xis the rainfall (in inches) on November 6of this year, and Yis the rainfall at the same location on November 6 of next year.
(b) Xis the amount of rainfall today, and Y is the rainfall at the same location tomorrow.
(c) Xis today's rainfall at the airport in Orlando, Florida, and Y is today's rainfall at Disney World just outside Orlando.

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.
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(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.

Spell-checking Refer to Exercise 3. Calculate and interpret the standard deviation of the random variable X. Show your work

Benford’s law and fraud Refer to Exercise 13. It might also be possible to detect an employee’s fake expense records by looking at the variability in the first digits of those expense amounts.

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