<p> Math 115A Test 2 Review Test 2 – Wednesday, April 29th</p><p>1. $5000 is invested into a bank account that offers an annual percentage rate of 2.9%. Find the future value of this money after 5 years, and the effective annual yield (round to three decimal places after converting to a percent), if interest is compounded:</p><p> a. Yearly b. Quarterly c. Monthly d. Daily e. Continuously</p><p>2. Suppose $6400 is invested in an account for 14 years where the interest is compounded quarterly. There is $8250 in the account after 14 years. What is the annual percentage rate? What is the corresponding yield? </p><p>3. How much time is required for $5200 to grow to $7400 in an account where the interest rate of 7.1% is compounded continuously? Round to the nearest month. </p><p>4. A finite random variable X can take on 4 distinct values. Below is a table with X and its probability mass function, fX ( x ). Answer the following: x -4 1 2 4.7 fX ( x ) .2 .25 ? .4 a. What is P(X = 1)? b. What is P(X ≤ 2.7)? c. What is P(X < 0)? d. What is P(X = 1.5)?</p><p>5. The Heart Association claims that only 15% of U.S. adults over 30 can pass the President’s Physical Commission’s minimum requirements. Suppose that 5 adults over 30 are randomly selected, and each is given the fitness test. Let X be the random variable that records the number of adults that pass the test. a. What distribution best describes X ? b. Find the probability that at least 2 adults pass the test. c. Find the probability that no adult passes the test. d. Find E(X ) . Explain E(X ) in words. e. Sketch the c.d. f . of X 6. You run a small baseball memorabilia shop and the only customer in the store just left. Suppose you know (somehow) that the arrival of the next customer is closely modeled by an exponential distribution. Also, suppose that the average time elapsed before the next customer arrives is 10 minutes. </p><p> a. Find the probability that the next customer arrives within 6 minutes. </p><p> b. Find the probability that the next customer arrives sometime after 3 minutes. </p><p> c. Find the probability that the next customer arrives exactly 2 minutes after the previous customer left. </p><p>2x 7. Let X be an exponential random variable with p.d.f. given by fX ( x ) 2 e . </p><p> a. Find the c.d.f. FX ( x ) </p><p> b. Determine P(2  X  4)</p><p>8. The c.d.f. of some random variable Y is given below. </p><p>0 if y  0  0.01 if 0  y  1 0.05 if 1  y  2  FY (y)  0.25 if 2  y  3 0.60 if 3  y  4  0.88 if 4  y  5  1.00 if y  5</p><p> a. Find the values of the p.m.f. of Y.</p><p> b. Create a graph of the p.m.f. of Y.</p><p> c. What value of Y is most likely?</p><p> d. What value of Y is least likely?  1 2 0  x   3   1 2 9. a. Sketch a graph of f X x   6x  4  x   3 3 0 otherwise   Identify at least 3 ordered pairs on your graph.</p><p> b. Show the function in part a. represents a probability density function.</p><p>1 2 c. Find P(  X  ) 2 3</p><p>10. A dart is thrown at a number line in such a way that it always lands in the interval 1,25. Let X be a uniform random variable that represents the real number the dart hits. Find the following: a. the c.d.f. and the p.d.f. for X b. P5  X  12 c. The probability the dart hits a number that is at least 7. d. The probability the dart hits the number 7.</p><p>11. A class of 30 students took a test. The scores of 10 of these students is shown below. Student Score Student Score 1 95 6 45 2 83 7 82 3 88 8 78 4 76 9 92 5 62 10 71</p><p>Let X be the random variable that represents the test score of a student chosen at random. a. Give an approximation for E(X). b. Give an approximation for P(X ≤ 80). </p>