Discrete Mathematics FINAL REVIEW Name Per. Evaluate and simplify the following completely, Show all your work. 1. 5! 2. 7! 42 3. 9!4! 3!10! 4. 24!19! 22!21! 5. 4! (7 5)! 6. 46! 45!23 7. 9 5!3! 18 2!4! 8. 14! (14 2)!2! 9. 2! (201 199)! 10. 19 C 7 11. 7 C 5 12. 12 C 12 13. 11 P 7 14. 100 P 2 15. 24 P 20 Solve the following problems. 16. A person can purchase a car with 5 different colors, three different trim packages, and two option packages. How many possibilities car can a person chose from? 17. How many different PIN numbers can be made using 6 digits 0-9, if the first cannot have a zero? 18. How many ways can first through third prizes be awarded to 75 contestants? 19. How many different ways can 15 students be chosen for the three main characters in a play?
20. How many distinct ways can the letters in the word WEST LINN be arranged? 21. How many distinct ways can the letters in the word STATISTICS be arranged? 22. How many ways can five airplanes line up for departure on the runway? 23. What is the probability of rolling a 6 on a 6 sided dice? 24. What is the probability of rolling a number less than 5 on a 6 sided dice? 25. What is the probability of rolling less than 3 or greater than or equal to a 7 on a 10 sided dice? 26. What is the probability of rolling a 4 or a 5 on a 6 sided dice? 27. What is the probability of not rolling a 1 or a 3 on a six sided dice? 28. What is the probability of rolling a 5 twice in a row on a six sided dice? 29. What is the probability of being dealt a face card from a 52 card deck? 30. What is the probability of drawing a red card or a 7 from a 52 card deck?
31. What is the probability of drawing a spade or a not a face card from a 52 card deck? 32. What is the probability when drawing three cards from a 52 card deck that all three are hearts? 33. What is the probability when drawing three cards from a 52 card deck that the first two are hearts and the last is not a heart? 34. A coin is tossed and a die is rolled. What it the probability of getting a. A head and a number greater than 4? b. A tail and a number less than 5? 35. You have a bag with seven red balls, four blue balls and three green balls. a. What is the probability of pulling a green ball? b. What is the probability of pulling a red or blue ball? c. What is the probability of pulling yellow ball? d. What is the probability of not pulling a blue ball? e. What is the probability of pulling a red ball and then (with replacement) drawing a red ball? f. What is the probability of pulling a red ball and then (without replacement) drawing a red ball? g. What is the probability of pulling a green ball, then a red ball then a blue ball (without replacement)? 36. The probability that a region prone to flooding will flood in any single year is 1/10. a. What is the probability of a flood two years in a row? b. What is the probability of no flooding for ten consecutive years?
37. What is the probability out of students; Sam, DJ, Levi, Jose, Frank, Tina and Bill a. That Bill would be last? b. That Sam or Levi were first? c. That DJ was first and Frank or Tina were last? d. That someone with an a in their name was first? 38. What is the formula for Mean? 39. What is the Median of a data set? 40. What is the Mode of a data set? 41. How do you calculate the Range of a data set? 42. What is the Standard Deviation of a data set? 43. For the data in the below calculate the 11 17 12 13 12 16 15 Mean Median Mode Midrange Range Standard Deviation 44. For the data in the below calculate the 27.5 27 29 28.2 27.5 27.2 28.8 Mean Median Mode Midrange Range Standard Deviation
45. A doctor randomly selects 18 of his 20-29 year-old patients and obtains the following data regarding their serum HDL cholesterol: 70 56 48 48 53 52 36 49 32 58 62 45 38 70 45 51 66 48 Calculate the sample- Mean Median Mode Midrange Range Standard Deviation 46. The frequency distribution table shows the rubric scores from a project for all of the student in a class. Calculate the Mean Median Mode Score Frequency 1 2 2 4 3 5 4 7 5 6 6 4 7 3 47. The frequency distribution table shows the student scores. Calculate the Mean Median Mode Score Frequency 1 1 2 1 3 2 4 5 5 7 6 9 7 8 8 6 9 4 10 3
48. What is a normal distribution? 49. What is the empirical rule? 50. What graph can we make from a frequency distribution table? 51. What is the definition of z-score? 52. SAT Math scores have a bell shaped distribution with a mean of 518 and a standard deviation of 114. a. What percentage of SAT scores is between 404 and 632? b. What percentage of SAT scores is less than 404 or greater that 632? c. What percentage of SAT scores is greater than 746? 53. A student scores 70 on an arithmetic test and 66 on a vocabulary test. The scores for both test are normally distributed. The arithmetic test has a mean of 60 and standard deviation of 20. The vocabulary test has a mean of 60 and a standard deviation of 2. On which test did the student have a better score? 54. The mean weight of newborn infant is 7 pounds and standard deviation is 0.8 pounds. The weights of newborn infants are normally distributed. Find the z score for a weight of a. 9 pounds b. 7 pounds c. 6 pounds
Assume 55-61 are normally distributed 55. Scores on a history test have average of 80 with standard deviation of 6. What is the z-score for a student who earned a 75 on the test? 56. The weight of chocolate bars from a particular chocolate factory has a mean of 8 ounces with standard deviation of.1 ounce. What is the z-score corresponding to a weight of 8.17 ounces? 57. Books in the library are found to have average length of 350 pages with standard deviation of 100 pages. What is the z-score corresponding to a book of length 80 pages? 58. The temperature is recorded at 60 airports in a region. The average temperature is 67 degrees Fahrenheit with standard deviation of 5 degrees. What is the z-score for a temperature of 68 degrees? 59. A group of friends compares what they received while trick or treating. They find that the average number of pieces of candy received is 43, with standard deviation of 2. What is the z-score corresponding to 20 pieces of candy? 60. The mean growth of the thickness of trees in a forest is found to be.5 cm/year with a standard deviation of.1 cm/year. What is the z-score corresponding to 1 cm/year? 61. A particular leg bone for dinosaur fossils has a mean length of 5 feet with standard deviation of 3 inches. What is the z-score that corresponds to a length of 62 inches?
62. An airport is studying the noise levels of jets during takeoff as they pass over a neighborhood. They find that at the present time the mean noise level is 103 decibels and the standard deviation is 5.4 decibels. The distribution of noise levels for all jets during takeoff over this neighborhood has a normal distribution. a. What proportion of these jets have a noise level of 95 decibels or less when taking off over this neighborhood? b. What is the probability one jet would have a noise level that is between 100 and 110 decibels? c. The airport would like to have 99% of all jets taking off over this neighborhood to have a noise level of 100 or less. What would the mean noise level have to be in order to achieve this goal? Assume the standard deviation would remain the same.
63. A linear regression of has a correlation coefficient of -.957 a. Is this a strong or weak correlation? b. Is this a positive or negative correlation? 64. Which graph shows no correlation? 65. Which graph shows a positive correlation? 66. Which graph shows a negative correlation? 67. Which graph shows a strong correlation?
68. For the data {3, 7, 8, 5, 12, 14, 21, 15, 18, 14} and {3, 7, 8, 5, 12, 14, 21, 13, 18} calculate - a. Min b. Q1 c. Median d. Q3 e. Max f. IQR g. Lower Fence h. Upper Fence 69. Which box plot goes with the first data set? 70. A smart phone with an original price of $299 is on sale at 25% off. a. What is the amount of the discount? b. What is the sale price of the phone? 71. A car with an original price of $25999 is on sale at 9% off. c. What is the amount of the discount? d. What is the sale price of the car? 72. 49.95 is what percent of 270? 73. 50 is what percent of 2550?
74. You borrow $5995 for three months at 8% simple interest. a. Find the amount of the interest paid. b. Find the future value of the loan. 75. You borrow $3500 from a friend and promise to pay back $3750 in four and half years. a. What simple interest rate will you pay? 76. In 23years you want to have $45,000 worth of remodeling done to your home. How much should you invest now, at 9% simple interest, to have enough money for the project? 77. At the time of a child s birth, $15,000 was deposited in an account paying 7.5% interest compounded quarterly. What will be the value of the account at the child s 18 th birthday? 78. You deposit $2100 in an account that pays 8% interest compounded semiannually. Your friend deposits $2200 in an account that pays 7.25% interest compounded monthly. a. Who will have more money in the account after 5 years? b. How much more? 79. In 1626, Peter Minut convinced the Wappinger Indians to sell him Manhattan Island for $24. If the Native Americans had put the $24 into a bank account paying compound interest at a 7.5% rate, how much would the investment be worth today if it was compounded semiannually? (t = 390 years) 80. How much should be deposited today in an account that earns 6.5% compounded quarterly to that it will be 10,000 in 10 years?
81. You decide to deposit $400 at the end of each month in an annuity that pays 6.5% compounded monthly. a. How much will you have after 5 years? b. How much will you make in interest after 5 years? c. How much will you have after 10 years? d. How much will you make in interest after 10 years? 82. You would like to have $12,000 in four years for a special vacation by depositing at the end of every month in an annuity that pays 8% and is compounded monthly. How much do you have to deposit each month? 83. How much should you deposit at the end of each month in an IRA that pays 4.5% compounded monthly to have $1,000,000 when you retire in 40 years? 84. The price of a home in West Linn is $459,000. The bank requires a 20% down payment and two points paid at the closing. You are trying to decide between a 30 year fixed rate at 3.75% vs. a 20 year fixed rate at 3.5%. a. What is the required down payment amount? b. How much are the points going to cost at closing? c. How much money do you need to close on the house? d. What is the monthly payment for each scenario? e. What is the total interest paid over the life of the loan for each scenario?
85. A student graduates from college with a loan of $127,000. The interest rate is 2.4% and the loan term is 20 years. a. What are the monthly payments? b. What is the total you paid once you pay it all back? c. What is the total amount paid in interest over the life of the loan? 86. You decide to go buy a car after you graduate. You are able to secure a loan of $31,000 at 3.5% interest rate. a. What is your monthly payment on a 5 year loan? b. What is the total amount of interest paid over the life of the loan?
A credit card calculates interest using the average daily balance method. The monthly interest rate is 2.1% of the average daily balance. The following transactions occurred during the September 1- September 30 billing period. Transaction Description Amount Previous balance: $2,712.14 September 1: Billing Date Sept. 5 th : Payment $300.00 credit Sept. 9 th : Charge, gas $45.62 Sept. 19 th : Charge, clothing $150.12 Sept. 23 rd : Charge, dining $56.50 Sept. 27 th : Charge, Duck tickets $140.00 Sept. 30 th : End of billing period 87. Find the average daily balance for the billing period. 88. Find the interest to be added to the bill for the next month. 89. The credit card requires a minimum down payment of 1/36 of your total balance. What is the minimum due next month?