2. Dee Pressants owns Dee’s Pharmacy located in a small medical office building. Dee estimates that 20% of her prescription business comes from referrals from Dr. Mel Practice. For the next 25 prescription customers, what is the probability that a. 6 or less were referred by Mel? b. Between 3 and 6 were referred by Mel? c. At least 4 were referred by Mel? d. Exactly 5 were referred by Mel? e. Dee makes $10 profit per prescription but has to pay Mel a $3 kickback on any referrals. What is the expected profit from the 25 customers?

I have the answers for these questions, according to my study guide. I don't understand how the answers were obtained, though, so please show work!

A) You are planning to take two exams. According to the records, the failure rates for the two exams are 15% and 25%, respectively. Additionally, 80% of the student who passed the exam 1 passed exam 2. (The 80% is based on the given condition.)

What will be the probability that you fail the 1st exam, if you did not pass the 2nd exam?

0.32

B) You are planning to take two exams. According to the records, the failure rates for the two exams are 15% and 25%, respectively. Additionally, 80% of the student who passed the exam 1 passed exam 2. (The 80% is based on the given condition.)

What is the probability that you will fail at most one exam?

0.92

C) You are planning to take two exams. According to the records, the failure rates for the two exams are 15% and 25%, respectively. Additionally, 80% of the student who passed the exam 1 passed exam 2. (The 80% is based on the given condition.)

Given that you have passed at least one of the exams, what is the probability that you have passed only one exam?

0.2609

1. Igor Beaver is a salesman for Planet of the Grapes, a medium sized winery near Solvang. Igor is going on a sales trip visiting 10 restaurants throughout Southern California. Historically, Igor convinces 30% of the restaurants he visits to stock and sell his wine. a. What is the expected number of restaurants that Igor will close a sale on this trip? b. Find the variance. What is the probability that on this sales trip Igor make sales at c. 4 restaurants or less? d. Between 2 and 4 restaurants? e. Exactly 4 restaurants? f. At least 5 restaurants? g. Igor gives each new client a gift. How many gifts should he take on the trip to be at least 99% sure that he has enough? h. Find and plot the probability distribution and cumulative distribution using Excel.

A business owner believed that a higher percentage of females than males bought items from her stores. To test her belief, she conducted a study. What might her research hypothesis be?

A. p = .5

B. p > .5

C. p > .5 (greater than or equal to symbol)

D. not enough information

Given:

What are the confidence limits (alpha = 0.05) for the true mean value of Y when X = 3?

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.