Dana Rand owns a catering company that prepares banquets and parties for both individual and business functions throughout the year. Rand’s business is seasonal, with a heavy schedule during the summer months and the year-end holidays and a light schedule at other times. During peak periods, there are extra costs; however, even during nonpeak periods Rand must work more to cover her expenses.

One of the major events Rand’s customers request is a cocktail party. She offers a standard cocktail party and has developed the following cost structure on a per-person basis.

When bidding on cocktail parties, Rand adds a 15 percent markup to this cost structure as a profit margin. Rand is quite certain about her estimates of the prime costs but is not as comfortable with the overhead estimate. This estimate was based on the actual data for the past 12 months presented in the following table. These data indicate that overhead expenses vary with the direct-labor hours expended. The $13 estimate was determined by dividing total overhead expended for the 12 months ($782,000) by total labor hours (58,500) and rounding to the nearest dollar.

Rand recently attended a meeting of the local chamber of commerce and heard a business consultant discuss regression analysis and its business applications. After the meeting, Rand decided to do a regression analysis of the overhead data she had collected. The following results were obtained.

Required:

2. Using data from the regression analysis, develop the following cost estimates per person for a cocktail party. Assume that the level of activity remains within the relevant range. a. variable cost per person? b. absorption (full) cost per person?

3. Dana Rand has been asked to prepare a bid for a 240-person cocktail party to be given next month. Determine the minimum bid price that Rand should be willing to submit. Minimum Bid Price?

4. What other factors should Dana Rand consider in developing the bid price for the cocktail party?

The chart below shows the correct answers for 4. in order.

If data set A has a larger standard deviation than data set B, what would be different about their distributions?

What is the value to us in the twenty-first century of having an accurate demographic picture of earlier centuries? Explain in detail and provide an example.

Choose the most appropriate statistic for measuring spread for the following data sets.

a.) A medical survey asks for patients' body fat percentages. Most people in the study had body fat percentages in the 20's, while a few had body fat percentages over 40. Which is the best measure of the spread of body fat percentages?

range, proportion, standard deviation, IQR, median, or mean

b.) The same survey also asks for patients' heights. Which is the best measure of the spread of height?

range, proportion, standard deviation, IQR, median, or mean

2. To see why this is relevant to our analysis of the arrangement of energy in degrees of freedom, first take a simple problem in the ways that you can arrange some cards from a deck.

a. Suppose you have only the numbered cards from one suit (say hearts) of one deck (numbered from Ace = 1 to 10). If you choose 4 of those cards at random, how many different sets of those cards could you get? (Order doesn't matter, so 10-9-8-7 is considered the same as 7-8-9-10.)

b. If you now select from the numbered cards from a different suit (say spades) of that deck and choose 3 of those cards at random, how many different sets of the spades could you get?

c. If you select BOTH four hearts and three spades at random, how many different sets of cards could you get?

Question 7

The following lists of data represent five separate departments' technicians overtime for a week. Which has the smallest standard deviation?

Select the correct answer below:

a)28, 26, 20, 17, 21, 29, 28, 28, 17, 22

b)14, 15, 15, 12, 11, 14, 11, 13, 14, 12

c)34, 26, 34, 26, 22, 34, 24, 26, 25, 24

d)21, 15, 14, 27, 21, 24, 27, 20, 20, 30

e)9, 17, 21, 9, 14, 18, 22, 10, 12, 16

Question 8

A deck of cards contains RED cards numbered 1,2,3,4,5,6 and BLUE cards numbered 1,2,3. Let R be the event of drawing a red card, B the event of drawing a blue card, E the event of drawing an even numbered card, and O the event of drawing an odd card.

Drawing the Blue 2 is an example of which of the following events? Select all correct answers.

Select all that apply:

B AND O

R OR E

E′

B′

R AND E

O′

B AND E

Question 9

If A and B are events with P(A)=0.2, P(A OR B)=0.62, and P(A AND B)=0.18, find P(B).

Provide your answer below:

Question 10

The probability of buying a movie ticket with a popcorn coupon is 0.608. If you buy 10 movie tickets, what is the probability that 3 or more of the tickets have popcorn coupons? (Round your answer to 3 decimal places if necessary.)

Provide your answer below:

P(X greater than or equal to 3)=

Question 11

At a certain company, the mentoring program and the community outreach program meet at the same time, so it is impossible for an employee to do both. If the probability that an employee participates in the mentoring program is 0.51, and the probability that an employee participates in the outreach program is 0.21, what is the probability that an employee does the mentoring program or the community outreach program?

Provide your answer below:

Question 12

A grain elevator measures the weight of each truck that delivers grain to their site. What is the level of measurement of the data?

a)Nominal

b)Ordinal

c)Interval

d)Ratio

Question 13

Let W be the event that a randomly chosen person works for the city government. Let V be the event that a randomly chosen person will vote in the election. Place the correct event in each response box below to show:

Given that the person works for the city government, the probability that a randomly chosen person has will vote in the election.

P(_ _ )

Question 14

Carlos and Devon both accepted new jobs at different companies. Carlos's starting salary is $42,000 and Devon's starting salary is $40,000. They are curious to know who has the better starting salary, when compared to the salary distributions of their new employers.

A website that collects salary information from a sample of employees for a number of major employers reports that Carlos's company offers a mean salary of $52,000 with a standard deviation of $8,000. Devon's company offers a mean salary of $48,000 with a standard deviation of $5,000.

Find the z-scores corresponding to each of their starting salaries. Round to two decimal places, if necessary.

Provide your answer below:

Carlos's z-score:

Devon's z-score:

Question 15

A deck of cards contains RED cards numbered 1,2,3,4,5, BLUE cards numbered 1,2,3,4,5,6, and GREEN cards numbered 1,2. If a single card is picked at random, what is the probability that the card is GREEN?

Select the correct answer below:

6/13

3/13

5/13

2/13

12/13

10/13

How do I do  independent t test on the data set below and how do I know if its pooled t test or unrolled t test?

Health question for reference: to what extend does the age of MI patients vary by gender

Standard deviation: male = 13.944 female= 13.939

mean: male 65.353 female=73.628

Male female

65   88
77   81
78   82
76   66
40   81
83   73
58   64
43   53
39   69
66   67
61   89
49   85
85   81
54   85
82   84
68   83
78   76
56   77
72   84
50   43
75   87
61   70
48   64
82   59
62   91
39   60
45   80
65   72
68   73
73   85
64   80
80   79
74   48
80   32
92   86
51
41
90
83
61
64   
82
48
63
81
52   
65   
74
62
71
73
43
80
72
57
76
53
44
71
64
86
60
63
74
56

7. A certain sports car model has a 0.07 probability of defective steering and a 0.11 probability of defective brakes. Erich S -E just purchased one of the models. If the two problems are statistically independent, determine the probability

a. Erich’s car has both defective steering and defective brakes.

b. Erich’s car has neither defective steering nor defective brakes.

c. Erich’s car has either defective steering only or defective brakes only (meaning exactly one of the two, but not both, defects).

5. Arsalaan A., a well-known financial analyst, selected 50 consecutive years of U.S. financial markets data at random. For 11 of the years, the rate of return for the Dow Jones Industrial Average [DJIA] exceeded the rates of return for both the S&P 500 Index and the NASDAQ Composite Index. For 8 of the years, the rate of return for the DJIA trailed the rates of return for both the S&P 500 and the NASDAQ. For 21 of the years, the rate of return for the DJIA trailed the rate of return for the S&P 500. Over the 50 years,

a. determine the probability the rate of return for the DJIA trailed the rate of return for the NASDAQ.

b. determine the probability the rate of return for the DJIA trailed the rate of return for at least one of the other two Indexes.

c. determine the probability the rate of return for the DJIA trailed the rate of return for the S&P 500 given it trailed the rate of return for the NASDAQ.

d. determine the probability the rate of return for the DJIA exceeded the rate of return for the S&P 500 given it exceeded the rate of return for the NASDAQ.

Let X have a binomial distribution with parameters

n = 25

and p. Calculate each of the following probabilities using the normal approximation (with the continuity correction) for the cases

p = 0.5, 0.6, and 0.8

and compare to the exact binomial probabilities calculated directly from the formula for

b(x; n, p).

(Round your answers to four decimal places.)

(a)

P(15 ≤ X ≤ 20)

(b)

P(X ≤ 15)

(c)

P(20 ≤ X)

Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wherever appropriate. (Round your answers to four decimal places.) (a) P(0 ≤ Z ≤ 2.13) (b) P(0 ≤ Z ≤ 1) (c) P(−2.20 ≤ Z ≤ 0) (d) P(−2.20 ≤ Z ≤ 2.20) (e) P(Z ≤ 1.93) (f) P(−1.15 ≤ Z) (g) P(−1.20 ≤ Z ≤ 2.00) (h) P(1.93 ≤ Z ≤ 2.50) (i) P(1.20 ≤ Z) (j) P(|Z| ≤ 2.50)

A particular poll tracks daily the percentage of citizens from a certain country who approve or disapprove of the job the President is doing. Daily results are based on telephone interviews with approximately 1400 national adults. The poll reported that 50​% of adults approve of the President doing his job. A media outlet claimed the true proportion to be 52​%. Does the poll contradict this​ claim? Complete parts a through c. ​a) Test the appropriate hypothesis. Find a 95​% confidence interval for the sample proportion of adults in the country who approved of the​ President's performance. Check conditions. Which conditions for the confidence interval have been​ met? Select all that apply. A. ​Success/Failure Condition B. ​10% Condition C. Randomization Condition Let p be the proportion of adults in the country who approved of the​ President's performance. What are the null and alternative​ hypotheses? Upper H 0​: p ▼ greater than equals less than not equals nothing vs. Upper H Subscript Upper A​: p ▼ equals greater than less than not equals nothing ​(Type integers or decimals. Do not​ round.) Find the 95​% confidence interval. left parenthesis nothing comma nothing right parenthesis ​(Round to three decimal places as​ needed.) ​b) Does your confidence interval provide evidence to contradict the​ claim? Select the correct choice below and fill in the answer box to complete your choice. ​(Type an integer or a decimal. Do not​ round.) A. Since nothing is within the​ interval, the confidence interval does not provide evidence that contradicts the media​ outlet's claim. B. Since nothing is within the​ interval, the confidence interval provides evidence that contradicts the media​ outlet's claim. C. Since nothing is not within the​ interval, the confidence interval provides evidence that contradicts the media​ outlet's claim. D. Since nothing is not within the​ interval, the confidence interval does not provide evidence that contradicts the media​ outlet's claim. ​c) What is the significance level of the test in​ b? Explain. Select the correct choice below and fill in the answer box to complete your choice. ​(Type an integer or a decimal. Do not​ round.) A. The significance level is alphaequals nothing because the test is a​ two-tail test based on a 95​% confidence interval. B. The significance level is alphaequals nothing because the test is a​ one-tail test based on a 95​% confidence interval. C. The significance level is betaequals nothing because the test is a​ two-tail test based on a 95​% confidence interval. D. The significance level is betaequals nothing because the test is a​ one-tail test based on a 95​% confidence interval.

Consider the following heart disease mortality data from two hypothetical countries, including a low-income and high-income country.

A. Use these data to calculate the overall crude death rates from heart disease in the hypothetical high and low income countries.

B. Based on these data, do you think that it is better to compare the heart disease death rates in the two countries using the overall crude rate or the age-standardized rate for each country? Briefly justify your answer.

An online account password for a certain website consists of eight characters, where at least one must be a digit (i.e. a number from 0-9).

a. How many different passwords are possible if only lowercase letters and digits can be used?

b. How many different passwords are possible if a user wants to include single capital letter somewhere in their password?

c. If a computer program randomly generates eight characters (such that each could be either a digit or any lowercase letter), what is the probability that a valid password is generated?

Let ? and ? be two independent uniform random variables such that ?∼????(0,1) and ?∼????(0,1).

A) Using the convolution formula, find the pdf ??(?) of the random variable ?=?+?, and graph it.

B) What is the moment generating function of ??