1. Two fair dice are tossed, and the face on each die is observed.

   1. Use a tree diagram to find the 36 sample points contained in the sample space.

   2. Assign probabilities to the sample points in part a.

   3. Find the probability of each of the following events:

      A = {3 showing on each die}
      B = {sum of two numbers showing is 7}
      C = {sum of two numbers showing is even}

   4. Also, for events A, B, and C, which one is simple event, which one is compound event?

   5. Event D= ?" , Event D and event C independent or not? Event D and event B mutually exclusive or not?

   6. Consider event D and event C, Find the probability of each of the following events: ?(D ∩ ?), p(D ∪ ?), ?(?|?), ?(?/|?/), ?(?/ ∩ ?/)

Harper Mining Ltd is considering to invest in one of the two following equipment. Each equipment will last 5 years and have no salvage value at the end. The company’s required rate of return for all investment projects is 7%. The cash flows of the projects are provided below. Equipment 1 Equipment 2 Cost $150,000 $165,000 Future Cash Flows Year 1 Year 2 Year 3 Year 4 Year 5 56,000 53,000 65,000 55,000 43,000 67,000 74,000 62,000 65,000 53,000 Required: a) Identify which option of equipment should the company accept based on net present value (NPV) method. (Note: All answers should be rounded up to 2 decimal places) ANSWER: b) Identify which option of equipment should the company accept based on discounted pay back method. ANSWER:

Question 4

Harper Mining Ltd is considering to invest in one of the two following equipment. Each equipment will last 5 years and have no salvage value at the end. The company’s required rate of return for all investment projects is 7%. The cash flows of the projects are provided below.

Required: a) Identify which option of equipment should the company accept based on net present value (NPV) method. (Note: All answers should be rounded up to 2 decimal places) ANSWER: b) Identify which option of equipment should the company accept based on discounted pay back method.

Which of the following best indicates the components of a vector that measures 30 m at 135°?

a)<21, 21> m

b)<-21, 21> m

c)<21, -21> m

d)<-21, -21> m

A student runs off of a diving platform with a speed of 2.5 m/s and hits the water 0.8 seconds later. What is the height of the platform?

Vector A has components A = <-2, 5> m/s and vector B has components B = <6, -2> m/s. What is the magnitude of vector C if C = A + B?

A student fires a bullet horizontally from a gun. Which statement is most accurate?

Which of the following is an example of a vector measurement?

A person driving through a field has velocity components that are 30 m/s west and 20 m/s south. What is the approximate direction of the overall velocity?

A student kicks a ball that is initially at rest on the ground. The ball leaves the student's foot with some velocity v at an angle θ. When the ball is at its maximum height, which statement is most accurate?

1. The following data represent the scores on a test for 36 students in a Sociology class, followed by a stem plot for the data.

65 76 83 81 74 78 41 57 82 50 90 81 63 68 80 85 76 73 79 48 80 75 72 70 75 74 94 87 81 78 64 83 77 72 79 86

4 1 8 5 0 7 6 3 4 5 8 7 0 2 2 3 4 4 5 5 6 6 7 8 8 9 9 8 0 0 1 1 1 2 3 3 5 6 7 9 0 4   

X = ______________________________________________________

ON ALL OF THE FOLLOWING PROBLEMS, SHOW ALL WORK AND LABEL YOUR ANSWERS WITH THE APPROPRIATE UNITS. LABEL ALL AXES ON ANY GRAPHS.

a. Find: median mode(s) range





------------------------------------------------------------------------------------------------------------------------------------------- b. Find and interpret the value for Q1. Show all work.
value of Q1 interpretation







------------------------------------------------------------------------------------------------------------------------------------------- c. Find the values ONLY of Q3 and P85. Show all work.
value of Q3 value of P85

(#1 cont’d)
!!!! DON’T FORGET TO PUT UNITS ON YOUR ANSWERS AND LABEL AXES ON GRAPHS !!!!


d. Give a five-number summary e. Construct a box plot for the test scores. for the test scores.

position value
__________ _____________
__________ _____________
__________ _____________
__________ _____________ _____________________________________________
__________ _____________

----------------------------------------------------------------------------------------------------------------------------------------------- f. Calculate the fences and list the outlier(s) in this set of scores. Construct a modified box plot to clearly show the outlier(s).

calculations lower fence ___________
upper fence ___________
outliers ________________






-------------------------------------------------------------------------------------------------------------------------------------------- g. Construct a modified box plot to clearly show the outlier(s). Label ALL critical positions with their corresponding values.










___________________________________________________________________

2. A random sample of 8 of the tests was chosen and their scores are given below. Calculate the sample mean, the sample variance and the sample standard deviation. Show all work.

78 64 81 75 50 85 79 72

mean








--------------------------------------------------------------------------------------------------------------------------------------------------
variance   

























-------------------------------------------------------------------------------------------------------------------------------------------------- standard deviation

3. The five number summary and the modified box plot for a set of test scores are given below.

five number summary: 33 68 80 86 97

  

modified box plot: 68 80 86 33 38 40 44 _______________________ 97

* * * | | _______________________ ______________________________________________________________________________________ 30 40 50 60 70 80 90 100 test scores   


X = _____________________________________________________________



a. What percent of the students scored at least an 86? ________________


b. What percent of the scores is between 33 and 80? ________________


c. The score of 80 is which of the following? mean median Q1 Q3


d. What percent of the scores is 80 or less? ________________


e. The minimum score for this distribution is ____________ and the maximum is _____________ .


f. List all outliers. ___________________________________


g. What is the value of Q3? ______________


h. Find the fences. Show all work. lower _____________ upper _____________

4. The average height of a 6th grade boy is 58 inches with a standard deviation of 2 inches. The average height of a 9th grade boy is 65 inches with a standard deviation of 3 inches. Both height distributions are bell-shaped.

a. If a 9th grade boy is 60 inches, which of the following is true based on the z-score for his height? Show work.
_____ His height is 1.67 inches below the mean. _____ His height is 1.67 inches above the mean. _____ His height is 1.67 standard deviations below the mean. _____ His height is 1.67 standard deviations above the mean.
-------------------------------------------------------------------------------------------------------------------------------------------------- b. If a 6th grade boy is 55 inches, which of the following is true based on the z-score for his height? Show work.
_____ His height is 1.5 inches below the mean. _____ His height is 1.5 inches above the mean. _____ His height is 1.5 standard deviations below the mean. _____ His height is 1.5 standard deviations above the mean.
-------------------------------------------------------------------------------------------------------------------------------------------------- c. Who is taller for his age: the 55-inch tall 6th grade boy or the 60-inch tall 9th grade boy? _____ The 9th grader is taller because his height is farther from the mean than the 6th grader’s. _____ The 9th grader is taller for his age because 60 inches is greater than 55 inches. _____ The 6th grader is taller because his height is closer to the mean than the 9th grader’s. _____ The 6th grader is taller because his height is not as far below the mean as the 9th grader’s.

-------------------------------------------------------------------------------------------------------------------------------------------------- d. Using the Empirical Rule, approximately ______ percent of 9th grade boys have heights between 59 inches and 71 inches. Show work to support your answer.







-------------------------------------------------------------------------------------------------------------------------------------------------- e. Using the Empirical Rule, approximately 99.7% of 6th grade boys fall between heights of _______________ and ______________. Show work to support your answer

The rate of reduction of [Co(NH3)5(OH2)]3 by Cr(II) is seven orders of magnitude slower than reduction of its conjugate base, [Co(NH3)5(OH)]2, by Cr(II). For the corresponding reductions with [Ru(NH3)6]2, the two differ by less than a factor of 10. What do these observations suggest about their mechanisms?

Suppose you are considering an investment in two bonds. Bond A has a duration of eight years and a market price of $950, and a bond B has a duration of four years and a market price of $1050. How should you invest $10 000 in these bonds if you have a desired holding period of seven years and wish to minimise interest rate risk?

Five people on the basement of a building get on an elevator that stops at seven floors. Assuming that each has an equal probability of going to any floor, find

(a) the probability that they all get off at different floors; (3 POINTS)

(b) the probability that two people get off at the same floor and all others get off at different floors. (4 POINTS)

. Suppose that an investor with a five-year investment horizon is considering purchasing a seven-year 9% coupon bond selling at par. The investor expects that he can reinvest the coupon payments at an annual interest rate of 9.4% and that at the end of the investment horizon two-year bonds will be selling to offer a yield to maturity of 11.2%. What is the five-year total return for this bond?

Data set

87 52 57 51 85 53 46 72 42 83

41 33 98 48 35 87 46 60 75 36

62 32 35 54 27 47 43 86 63 70

39 48 39 32 74 73 67 44 82 89

23 34 38 46 92 44 57 88 49 28

58 40 21 29 42 49 60 26 86 58.

For the given data set, create a frequency distribution with 7 classes. on separate page(s), provide answers for the following: n=, max, min, range, class width, upper and lower class limits, upper and lower class boundaries, class mid points, frequency distribution with histogram and frequency polygon, relative distribution with pareto chart, cummulative distribution with Ogive. submit a summary page(s) with your conclusions and graphs. submissions must be neat and professinal. points may be deducted for sloppy and unprofessional papers. please include your work at the end of the submission.