Business Mathematics ISample Midterm Examination 2This test is only presented as a sample of the types of questions that might appear on an examination. The instructor of each section will set his or her own examinations, which may differ from the sample in both length and content.Show all of the steps and all of the work that you use to solve each problem. A list of formulas that you may find useful is provided on the last page of this test.1. (8 points) $2,000 is left in an account that pays 6% interest. How much money is in the account atthe end of 5 years, if interest is compounded quarterly?2. (9 points) If interest is compounded continuously at 5%, what is the present value of a payment of$5,000 two years from now?3. (8 points) What does the Histogram function in Excel do, where do you find it, and how is it used toanalyze data?4. (9 points) Check the correct space for each random variable.(i) X is the number of business days in December, 2005 during which the S & P 500 Index will closehigher than it did on the preceding business day. Is X ___ a finite random variable or ___ a continuous randomvariable?(ii) X is the time, measured in days and parts of days, from Noon on November 30, 2005 until the nexttime that you are in an automobile which is involved in an accident. Is X ___ a finite random variable or ___ acontinuous random variable?(iii) X the distance, measured in yards and parts of yards, that a toy car will travel before its battery goesdead. Is X ___ a finite random variable or ___ a continuous random variable?5. (8 points) For each graph, select the statement that is most likely to be correct.a. The function is a probability mass function for a discrete random variable.b. The function is a probability density function for a continuous random variable.c. The function is a cumulative distribution function for a discrete random variable.d. The function is a cumulative distribution function for a continuous random variable.e. None of the above.© 2001 by The Arizona Board of Regentsfor The University of Arizona.All rights reserved.- Business Mathematics I, Sample Test 2: page 2 -(i)___ a. ___ b. ___ c. ___ d. ___ e.(ii) ___ a. ___ b. ___ c. ___ d. ___ e.(iii) Hint: look carefully at the numbers on the axes.___ a. ___ b. ___ c. ___ d. ___ e.(iv) ___ a. ___ b. ___ c. ___ d. ___ e.6. (8 points) A random variable T has the following values and probabilities.t 1 5 10 100P(T = t) 0.6 0.2 0.1 0.1(i) The p.m.f., fT has fT(5) = ___ . (ii) The p.m.f., fT has fT(7) = ___ .0 0.5 1 1.5 2 2.5 30.511 0 1 2 3 4 5 6 7 8 90.10.20.30 0.5 10.511.520 1 2 3 412- Business Mathematics I, Sample Test 2: page 3 -(iii) The c.d.f., FT has FT(5) = ___ . (iv) The c.d.f., FT has FT(7) = ___ .7. (8 points) Let X be the number of tails that occur in a set of 25 tosses of a fair coin.(i) Provide all possible information about the distribution of X.(ii) Compute E(X) and use your answer from Part i to justify your computation.8. (8 points) Y is an exponential random variable with an expected value of 10. Evaluate P(Y 12),rounded to 3 decimal places. Hint: what is the parameter, , for Y?9. (8 points) Let A be the age of a randomly selected student in your Business Mathematics I class.You find that the ages of the four students sitting in your row are 20, 21, 25, and 20 years. (i) Use this information to estimate E(A).(ii) Use this information to estimate FA(20).10. (8 points) Explain, in detail, how you would use Excel to generate a column of 5 integers, eachrandomly selected from 0, 1, , 9. The column is to start in Cell A1.11. (9 points) While using Excel, how would you use the IF function to return yes in Cell A2, if thenumber in Cell A1 is less than 3, and return no in Cell A2, if the number in Cell A1 is greater than or equal to 3?12. (9 points) (i) Consider a European call stock option on IBM that expires in 35 weeks, with a strikeprice of $150. Suppose that IBM currently sells for $130 and that the expected value of its price in 35 weeks is$139. Is the call option necessarily worthless? Explain your answer.(ii) Suppose that the only possible closing prices for IBM after 35 weeks are $130, $150, $160, and$170; and that each of these values are equally likely. What is the expected value of the option at its expiration?(iiI) In Class Project 2 on pricing a stock option, why do we convert the closing price data to ratiosbefore generating random samples?- Business Mathematics I, Sample Test 2: page 4 -FormulasF = Pert P = Fe-rt E(X) = np E(X) = tnnrFP 1tnnrPF 1 111nynr11
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