In a particular community, 65 percent of households include at least one person who has graduated from college. You randomly sample 100 households in this community. Let X=the number of households including at least one college graduate.

What is the probability that at most 82 households include at least one college graduate?

A stockbroker has a large number of clients. The proportion of clients with whom she does not communicate during a given month has the beta distribution with parameters α = 6 and β = 2. Determine the probability that, during a given month, the percentage of clients with whom the broker does not communicate will be

a) at least 60%.

b) between 70% and 80%.

A die is weighted so that rolling a 1 is two times as likely as rolling a 2, a 2 is two times likely as rolling a 3, a 3 is two times as likely as rolling a 4, a 4 is two times a likely as rolling a 5, and a 5 is two times as likely as rolling a 6. What is the probability of rolling an even number?

We have 95 students in a class. Their abilities/eagerness are uniform randomly distributed on a scale between 1 and 4; and at the end of the class they will be judged right and they will receive a grade corresponding to their ability/eagerness (corresponding to their performance). What is the probability that the class average will be between 2.8 and 4? How would this number change (if it does) for 120 students?

Problem 4) Five coins are flipped. The first four coins will land on heads with probability 1/4. The fifth coin is a fair coin. Assume that the results of the flips are independent. Let X be the total number of heads that result.

(hint: Condition on the last flip).

a) Find P(X=2)

b) Determine E[X]

18. TRUE OF FALSE: Payback is the number of years it takes for the project to pay for itself, without regard to the time value of money.

19. TRUE OF FALSE: The high profitability index means that the company will achieve the highest NPV per dollar of investment.

20. TRUE OR FALSE: NPV is the best method for capital rationing situations.

21. TRUE OR FALSE: In some cases, NPV and IRR will rank projects differently.

22. TRUE OR FALSE: Under capital rationing situations, a firm will not undertake all projects that are viewed as profitable; only those projects that will return the highest NPV for the limited capital available should be undertaken.

23. TRUE OR FALSE: In choosing between 2 mutually exclusive projects where only one can be undertaken because of limited capital, the project with the highest profitability index should be undertaken.

24. In deciding or choosing among capital projects to undertake:

a. Net Present value is the difference between investment cash outflows and cash inflows taking into account the time value of money using a discount rate, hurdle rate, or cost of capital.

b. Internal rate of return is the discount rate computed such that the net present value of the investment is zero.

c. Profitability index facilitates comparison of different sized investments.

d. All of the above is correct.

25. NPV and IRR are the soundest investment rules from a shareholder wealth maximization perspective:

a. Using NPV and IRR as the basis of choosing between mutually exclusive projects, if one accepted, the other must be rejected.

b. Using NPV and IRR as the basis of choosing between mutually exclusive projects, a project with an initial outlay of $1,000, Year end cash flow of $1,000, IRR of 20% and NPV of $91 will prevail over a project with an initial outlay of $50, Year end cash flow of $100, IRR of 100% and NPV of 41.

c. Using IRR, the choice in (b) above will be the opposite, that is, the project with an IRR of 100% will prevail.

d. All of the statements above are correct.

PLEASE ANSWER JUST QUESTION i, j, l. Thanks

Confidence   interval   for   a   mean   and   one-sample   t-test.   As   the world   warms,   the   geographic   ranges   of   species   might   shift   toward   cooler   areas.   Chen   et   al. (2011)   studied   recent   changes   in   the   highest   elevation   at   which   species   occur.   Typically, higher   elevations   are   cooler   than   lower   elevations.   Below   are   the   changes   in   highest elevation   for   31   taxa,   in   meters,   over   the   late   1900s   and   early   2000s.   (Many   taxa   were surveyed,   including   plants,   vertebrates,   and   arthropods.)   Positive   numbers   indicate   upward shifts   in   elevation,   and   negative   numbers   indicate   shifts   to   lower   elevations.   The   values   are displayed   in   the   accompanying   figure.

58.9,   7.8,   108.6,   44.8,   11.1,   19.2,   61.9,   30.5   12.7,   35.8,   7.4,   39.3,   24.0,   62.1,   24.3,   55.3   32.7, 65.3,   −19.3,   7.6,   −5.2,   −2.1,   31.0,   69.0   88.6,   39.5,   20.7,   89.0,   69.0,   64.9,   64.8
a.   What   is   the   sample   size   n?

b.   What   is   the   mean   of   these   data   points?   Remember   to   give   the   units.

c.   What   is   the   standard   deviation   of   elevational   range   shift?   (Give   the   units   as   well.)

d.   What   is   the   standard   error   of   the   mean   for   these   data?

e.   How   many   degrees   of   freedom   will   be   associated   with   a   confidence   interval   and   a   onesample   t-test   for   the   mean   elevation   shift?

f.   What   value   of   α   is   needed   for   a   95%   confidence   interval?

g.   What   is   the   critical   value   of   t   for   this   α   and   number   of   degrees   of   freedom?

h.   What   assumptions   are   necessary   to   use   the   confidence   interval   calculations   in   this   chapter?

i.   Calculate   the   95%   confidence   interval   for   the   mean   using   these   data.

j.   For   the   one-sample   t-test,   write   the   appropriate   null   and   alternative   hypotheses.

k.   Calculate   the   test   statistic   t   for   this   test.

l.   What   assumptions   are   necessary   to   do   a   one-sample   t-test?

m.   Describe   the   P-value   for   this   test   as   accurately   as   you   can.

n.   Did   species   change   their   highest   elevation   on   average?

In this assignment, the program will keep track of the amount of rainfall for a 12-month period. The data must be stored in an array of 12 doubles, each element of the array corresponds to one of the months. The program should make use of a second array of 12 strings, which will have the names of the months. These two arrays will be working in parallel. The array holding the month names will be initialized when the array is created using an initialization list (could also be created as an array of constants). The second array will hold doubles which will be the total rainfall for each month. Using a function, the program will prompt the user for the rainfall for each month (using both arrays) and store the value entered into the array with the rainfall totals; the other is used to display which month the program is asking for the rainfall total.

The output of the program will display the following once the data is all entered:

• The total rainfall for the year
• The average monthly rainfall
• The month with the highest amount of rainfall (must display the month as a string)
• The month with the lowest amount of rainfall (must display the month as a string)

The program must have the following functions:

• void CollectRainData(double [ ], string [ ], int);
  • Gets the user input for the rain totals for each month
  • Parameters array for rainfail totals, array of month names and size of arrays
• double CalculateTotalRainfall(double [ ], int);
  • Calculates the total rainfall from the array parameter.
• double CalculateAverage(double, int);
  • Calculates the Average rainfall
  • First parameter is the total rainfall, second is number of months
• double FindLowest(double [ ], int, int&);
  • Finds the month with the lowest amount of rainfall, returns this value
  • Provides the index of the lowest month in the last parameter.
• double FindHighest(double [ ], int, int&);
  • Finds the month with the highest amount of rainfall, returns this value
  • Provides the index of the highest month in the last parameter.

Pseudocode must be provided in the comment block at the top of the file. This must be done with Visual Studio 2019 comm edition C++

Table 3: Cars Sold per Day

For example, 35 of the days, no cars were sold. For 75 days one was sold.

1. How many days were used in this study?
2. Based on this study, what was the expected number of cars sold per day?
3. What is the probability of selling 5 cars in a day?
4. What was the variance in the expected number of cars sold per day?
5. What was the standard deviation in the expected number of cars sold per day?
6. What is your coefficient of variation for the sales?
7. How many cars were sold during the periods you are studying?
8. For the next 50 days, what will be the expected number of cars sold?

Let p be the (unknown) proportion of males in a town of 100, 000 residents. A political scientist takes a simple random sample of 100 residents from this town.

(a) Write down the exact pmf, as well as an approximate pmf, for the number of males in the sample. (They should both depend on p).

(b) If the number of males in the sample is 55 or more, the political scientist will claim that there are more males than females in the town. If the number of males in the sample is less than 55, he/she will claim that the number of males in the town is smaller or equal to that of females. What is approximately the probability that his/her claim will be correct if the true proportion of males in the town, p, is 50%? What if p = 55%?

(c) Report an approximate 68% confidence interval for p if 65 of the 100 residents in the sample are male.