1) Find the conditional probability of the indicated event when two fair dice (one red and one green) are rolled. The red one is 4, given that the sum is 9.

2)The Sad State Lottery requires you to select a sequence of four different numbers from 0 through 51. (Order is important.) You are a Winner if your sequence agrees with that in the drawing, and you are a Booby Prize Winner if your selection of numbers is correct, but in the wrong order. What is the probability of being a Booby Prize Winner?

Sales personnel for Skillings Distributors submit weekly reports listing the customer contacts made during the week. A sample of 65 weekly reports showed a sample mean of 18.5 customer contacts per week. The sample standard deviation was 5.6. Provide 90% and 95% confidence intervals for the population mean number of weekly customer contacts for the sales personnel.

90% Confidence interval, to 2 decimals:

( , )

95% Confidence interval, to 2 decimals:

( , )

Given the following probability distributions for variables X and Y:

P(x, y)X                  Y

0.4       100            200

0.6       200            100

a. E(X) and E(Y).

b. σX and σY.

c. σXY. d. E(X + Y).

e. Suppose that X represents the number of patients successfully treated for Malaria and Y represents the number of patients successfully treated for Tuberculosis. And medication A (first row in the table) has a 40% of effectiveness and medication B (second row in the table) has a 60% of effectiveness. Interpret and make statements based on the calculations you did.

A group of 5 friends are playing poker one night, and one of the friends decides to try out a new game. They are using a standard 52-card deck. The dealer is going to deal the cards face up. There will be a round of betting after everyone gets one card. Another round of betting after each player gets a second card, etc. Once a total of 7 cards have been dealt to each player, the player with the best hand will win. However, if any player is dealt one of the designated cards, the dealer collects all cards, shuffles, and starts over.

The designated cards are: 9 of Spades, 10 of Hearts, 2 of Diamonds, 7 of Clubs. The players wish to determine the likelihood of actually getting to play a hand without mucking the cards and starting over.

In how many ways can you deal the cards WITHOUT getting one of the designated cards?  (Hint: Consider how may cards are in the deck that are NOT one of the designated cards and consider how many cards need to be dealt in order for each player to have 7 cards.)

In how many ways can you deal each player 7 cards, regardless of whether the designated cards come out?

What is the probability of a successful hand that will go all the way till everyone gets 7 cards?     (Round your answer to 4 decimal places.)

Recall, while using your calculator, that E10 means to move the decimal place 10 places to the right.

An analyst at a local automotive garage wanted to see if there were relationships between repair time in hours (y) and months since last service(x1), type of repair(x2), whether it was a truck or car(x3), or the mileage of the vehicle(x4). Use a level of significance of 0.05.

1. What is the dependent variable?

2. What are the independent variables?

3. Run the regression analysis with the four independent variables. Write out the prediction equation.

4. From a global perspective is the model worth keeping? Why?

5. Evaluate the individual independent variables, circle the variables would you consider removing? Explain why?          X1                         X2                           X3                            X4

6. Rerun the regression analysis after removing the unnecessary independent variables. Write the regression equation:

7. What repair time will it take for a car with 90000 miles, not serviced for six months, and requires for electrical repairs?

A small business uses a website to sell clothing and accessories. the owners use data analytics and have determined , based on the past 6 months of web visit data, that on any given day the website receives an average of, μ=300 visits (hits) per day.

(a) Using Chebysheff's theorem find the Chebysheff Confidence interval,Iκ, which indicates the number of consumers that will visit the website at least 75% of the time (days).

(b) If the average purchase per customer is $50. Based on the results in part a , what daily revenue can the owners expect at least 75% of the days?

A large data sample from the past 8 club tournaments was analyzed by the club pro instructing stuff who determined the following statistics (in strokes)for the golf scores recorded in the tournaments.

Max Score=140 Min Score=70 Average Score=90 Standard Deviation=8

(a) Find the Max/Min standardized score for a golfer whose score=105

(b)Calculate the normalized score,N, for a golfer whose score=114

I want question 8 answered question 7 is posted because data from that question is required to answer 8

7. The following is the joint probability distribution of number of car crashes (C) and car make (M). C = 0 C = 1 C = 2 C = 3 C = 4 TOYOTA (M = 0) 0.35 0.065 0.05 0.025 0.01 OTHER (M = 1) 0.45 0.035 0.01 0.005 0.00 A. Report the marginal probability distribution for C B. What is the average number of car crash? C. What is the variance of the number of crashes? D. Calculate σCM and ρCM.

8. Suppose car manufacturers are penalized (P) on the basis of the following formula P = 60,000 + 6C – 2M Using your answers for Question 7, calculate the following A. The average penalty (P) B. The variance of penalty (P)

A statewide census examined the number of beds in households and reported a mean (μ) of 2.25 beds and standard deviation (σ) of 1.9 beds per household. But, since I live in a neighborhood with larger families, I have a hunch that the average number of beds in households will be higher in my neighborhood. To test this idea, I randomly picked 25 families in my neighborhood and surveyed them on the number of beds in their home. I would like to perform a Z test to see if the average number of beds in households in my neighborhood is significantly higher than the statewide average. The significance level for my Z test was set at α = .10.

a) What is the dependent variable in this study? b) What should be my null and alternative hypotheses? State each hypothesis using both words and statistical notation. Hint: I am interested in the idea of my neighbors having more beds per household than the state average, so the hypotheses would be directional. c) Calculate the sample mean. d) Calculate standard error (SE, which is the standard deviation of the sampling distribution) e) Calculate the Z statistic (which indicates where our sample mean is located on the sampling distribution) f) Specify whether the hypothesis test should be a two-tailed or a one-tailed test, and explain the rationale for the choice. g) Determine the critical value for Z h) Compare obtained Z and critical Z and then make a decision about the result of the hypothesis test: Explicitly state “reject” or “fail to reject” the null hypothesis i) Write a 1-2 sentence conclusion interpreting the results (you can simply restate the accepted hypothesis or explain it in another way) j) Calculate the raw and standardized effect sizes k) If the test was done with α level of .05, using the same directional hypotheses, what would be the critical Z value from the Z table? What would be the result of the hypothesis test (in terms of rejecting or failing to reject the null hypothesis)? l) Compare the hypothesis tests result when α = .05 and when α = .10. Were the results the same? Why or why not?

Use the given values of

n=2112

and

p=3/4

to find the maximum value that is significantly​ low,

muμminus−2sigmaσ​,

and the minimum value that is significantly​ high,

muμplus+2sigmaσ.

Round your answer to the nearest hundredth unless otherwise noted.

In the book Analysis of Longitudinal Data, 2nd ed., (2002, Oxford University Press), by Diggle, Heagerty, Liang,and Zeger, the authors analyzed the effects of three diets on the protein content of cow’s milk. The data shown here were collected after one week and include 25 cows on the barley diet and 27 cows each on the other two diets:

(a) What is the value of LSD for Barley+Lupins diet and Lupins diet? Use α=0.05.
Round your answer to three decimal places (e.g. 98.765).

(c) What is the absolute value of difference between mean protein content after Barley+Lupins diet and Lupins diet?
Round your answer to three decimal places (e.g. 98.765).

(d) Estimate the standard error for comparing the means using the graphical method. Use minimum sample size.
Round your answer to three decimal places (e.g. 98.765).

Sketch the area under the standard normal curve over the indicated interval and find the specified area. (Enter a number. Round your answer to four decimal places.) The area to the left of z = 0.42 is ?

We always seem to be focused on using statistics in Business decisions. Please think of some ways you can use statistics in your own decision making. For example, when we go on vacation as a family, we choose between many different types of travel. Using statistical analysis, I am able to come up with different pricing options.

A restaurant uses comment cards to get feedback from its customers about newly added items to the menu. It recently introduced homemade organic veggie burgers. Customers who tried the new burger were asked if they would order it again. The data are summarized in the table below. Which of the following would be an appropriate method for displaying the data shown in the​ table?

Response Frequency Definitely would 10 Most likely would 40 Maybe 12 Definitely would not 3

Possible Answers (please choose one)
Frequency Histogram
Box & Whisker Plot
Stem & Leaf Display
Relative Frequency Bar Chart

A business researcher conducted a survey of 500 women to determine preferences for types of automobiles. The types are shown below along with the number of women who prefer each type. Which of the following charts would be appropriate for displaying these​ data?

Type of Automobile Females Sedan 155 SUV 112 Van 125 Sports cars 55 Convertible 28 Other 25

Possible Answers (please choose one)
Histogram
Box & Whisker Plot
Stem & Leaf Display
Pie Chart

For the following situations, please write out null and alternative hypotheses.

a. Assuming m = 100, do children who watch more than three hours of TV per day have significantly lower IQs?

b. Assuming m = 100, a cognitive psychologist would like to know if the IQs of children who play outside at least three days a week are different from that of the population.

c. Assuming m = 50, write out the null and a non-directional alternative hypothesis.