MATH 1324 Review for Test 4 November 2016 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Prepare a probability distribution for the experiment. Let x represent the random variable, and let P represent the probability. 1) Three coins are tossed, and the number of tails is noted. 1) Give the probability distribution and sketch the histogram. 2) A class of 44 students took a 10-point quiz. The frequency of scores is given in the table. Number of Points Frequency 5 2 6 5 7 10 8 15 9 9 10 3 Total: 44 2) Find the expected value for the random variable. 3) x 2 3 4 5 P(x) 0.2 0.1 0.6 0.1 3) Find the expected value for the random variable x having this probability function. 4) 4) a = 18 b = 19 c = 20 d = 21 5) Suppose you buy 1 ticket for $1 out of a lottery of 1000 tickets where the prize for the one winning ticket is to be $500. What are your expected winnings? 5) Evaluate the expression. 6) 8 P 4 6) 7) 12 C 4 7) 1
Use the multiplication principle to solve the problem. 8) License plates are made using 2 letters followed by 2 digits. How many plates can be made if repetition of letters and digits is allowed? 8) 9) A restaurant offers 7 possible appetizers, 11 possible main courses, and 9 possible desserts. How many different meals are possible at this restaurant? (Two meals are considered different unless all three courses are the same). 9) 10) How many 4-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, if repetition of digits is not allowed? 10) 11) There are 12 members on a board of directors. If they must elect a chairperson, a secretary, and a treasurer, how many different slates of candidates are possible? 11) 12) There are 8 members on a board of directors. If they must form a subcommittee of 3 members, how many different subcommittees are possible? 12) 13) If the police have 8 suspects, how many different ways can they select 5 for a lineup? 13) 14) Three student representatives are to be chosen from a group of five students: Andrew, Brenda, Chad, Dorothy, and Eric. In how many different ways can the representatives be chosen if two must be male and one female? 14) 15) How many distinguishable permutations of letters are possible using the letters in the word CRITICS? 15) 16) 10 people are bowling: 3 use a black ball and 7 use a blue ball. How many different black and blue bowling ball sequences can occur on the rack? 16) A bag contains 6 cherry, 3 orange, and 2 lemon candies. You reach in and take 3 pieces of candy at random. Find the probability. 17) All cherry 17) 18) Find the number of ways of arranging 5 distinct items in a circle. 18) Find the requested probability. 19) A family has five children. The probability of having a girl is 1. What is the probability of 2 19) having exactly 3 girls and 2 boys? A die is rolled 20 times and the number of twos that come up is tallied. Find the probability of getting the given result. 20) More than three twos 20) In a certain college, 33% of the physics majors belong to ethnic minorities. Find the probability of the event from a random sample of 10 students who are physics majors. 21) Two or less belong to an ethnic minority. 21) 2
Find the probability of the event. 22) A 10-question multiple choice test has 4 possible answers for each question. A student selects at least 6 correct answers. 22) 23) On a hospital floor, 16 patients have a disease with a mortality rate of.1. Two of them die. 23) Find the interest. Round to the nearest cent. 24) $900 at 4% for 4 years 24) Find the exact interest. Use 365 days in a year, and use the exact number of days in a month. Round to the nearest cent, if necessary. 25) $3300 at 8% for 160 days 25) For the given bond, whose interest rate is provided, find the semiannual interest payment and the total interest earned over the life of the bond. 26) $10,000 FI National Corporation 18-year bond at 4.5% 26) Find the future value of the loan. 27) $600.00 loan at 8% for 5 months 27) Find the present value of the future amount. Assume 365 days in a year. Round to the nearest cent. 28) $19,000 for 2 months; money earns 5% 28) The given Treasury bill was sold in April of this year. Find (i) the price of the T-bill, and (ii) the actual interest rate paid by the Treasury. Round dollar amounts to the nearest cent and interest rates to the nearest thousandth. 29) Three-month $5000 T-bill with discount rate 0.120% 29) 30) How much must Harry's Hardware deposit at 10.5% interest for 240 days in order to earn $300.00 interest? Round to the nearest dollar. 30) 31) Tuition of $2700 is due when the spring term begins, in 9 months. What amount should a student deposit today, at 11%, to have enough to pay tuition? 31) 32) A note with a face value of $4300 was discounted at 3%. If the discount was $21, find the length of the loan in days. 32) 3
Answer Key Testname: MATH 1324 REVIEW FOR TEST 4 NOV 2016 1) 2) x P 0 1/8 1 3/8 2 3/8 3 1/8 Number 5 6 7 8 9 10 Probability.05.11.23.34.20.07 3) 3.6 4) 20 5) -$.50 6) 1680 7) 495 8) 67,600 9) 693 10) 840 11) 1320 12) 56 13) 56 ways 14) 6 15) 1260 16) 120 17).1212 18) 24 19).3125 20).433 21).3070 22).020 23).275 24) Interest = $144.00 25) $115.73 26) $225.00; $8100.00 27) $620.00 4
Answer Key Testname: MATH 1324 REVIEW FOR TEST 4 NOV 2016 28) $18,842.98 29) (i) $4998.50; (ii) About 0.12% 30) $4345 31) $2494.23 32) 60 days 5