Practice problems

1. Case Study: Motion Theater Releases Use

graphical methods to construct the following (do not write a report):

Movie Title	Open gross sales(Million)	Total Gross Sales(million)	Number of theatres	Weeks in release
Rouge one	155.08	532.18	4157	20
Finding Dory	135.06	486.30	4305	25
Civil war	179.14	408.08	4226	20
Seceret life of pets	104.35	368.38	4381	25
Jungle book	103.26	364.00	4144	24
Dealpool	132.43	363.07	3856	18
Zootopia	75.06	341.27	3959	22
Batman	166.01	330.36	4256	12
Suicide squad	133.68	325.10	4255	14
Sing	35.26	270.40	4029	20

(a) frequency (i.e., histogram or relative frequency) distribution graphs for all 4 variables

(hint: remember to use Sturges'Formula and Excel's Data Analysis tool).

(b) a scatter diagram to explore the relationship between opening gross sales and total

gross sales.

(c) a scatter diagram to explore the relationship between number of theaters and total grosssales.

(d) a scatter diagram to explore the relationship between weeks in release and total grosssales.

2.Amateur Golfer Scores. Scores turned in by an amateur golfer at the Bonita Fairways Gold Course in Bonita Springs Florida during the 2017 and 2018 are as follows:

2017: 74,78,79,77,75,73,75,77

2018: 71,70,75,77,85,80,71,79

1. Use the mean and standard deviation to evalute the golfers performance over the two year period
2. What is the primary differene in the performance between 2017 and 2018? What improvement , if any, can be seen in the 2018 scores?

3. Consider a sample with a men of 30 and a standard deviation of 5. Use Chebshev's theorem to determine the percentage of the data within each of the following ranges

A: 20 to 40

B: 15 to 45

C: 22 to 38

4. A wine taster is required to taste and rank three varieties of wine A, B, and C, accordingto the taster's preference.

(a) Identify all the possible rankings (note: order matters).

(b) If the taster had no ability to distinguish a difference in taste among the three wines,what is the probability that the taster will rank wine variety A as best? As least desirable?

5. The personnel manager for a commercial bank has interviewed five men and seven

women for four managerial training positions available with her bank. If the final selectionwill include two men and two women, how many different combinations are possible?

6. Use the data to answer the following questions.

An accounting firm believes that it may have to hire additional accountants to assist with the increased demand in tax advice for the upcoming tax season. Backen and hayes LLC has developed the following probability distribution for x= number of new clients seeking tax advice.

X 20 25 30 35 40 45 50

F(x) .05 .20 .25 .15 .15 .15. .10 .10

(a) Graph the probability distribution of X.

(b) Calculatesmallxand2/x

(c) Calculate the x+/xandx+2xintervals. What proportion of the

measurements will fall within these intervals? Does this result agree with Chebyshev's

Theorem? The Empirical Rule?

7. You are hoping to take advantage of an opportunity to operate a small business this

summer. In order to provide your services to potential customers, you will need to hire

one worker. If you hire a"hard-working" employee, you will make $5,000 in profit. If you

end up with a"lazy" employee, you will only make $1,000 in profit. There is an 80 percent

chance that you will hire a"hard-working" employee and a 20 percent chance that you will

hire a"lazy" employee. Suppose you have a utility function of the form = 3/4 where X is

the amount of profit you make.

(a) What is your expected utility this summer?

(b) Cindy is an employment consultant and an infallible judge of talent and character. After

an interview, she can state with certainty whether the worker will be"hard-working."

Would you be willing to pay her $1,000 for her services? Explain.

(c) What is the maximum amount you would be willing to pay Cindy?