Name Block Date Algebra 2- Statistics and Probability Chapter Review Statistics- Calculator Allowed with Applicable Work For exercises 1-4, tell whether the data that can be gathered about each variable are categorical or numerical. 1. months of the year 2. grade point averages 3. a commuter s mode of transportation 4. a person s annual salary For questions 5-6 a survey situation is described. Identify what type of graph would best describe the resulting data. 5. Suppose a survey is to be conducted to find out the average number of hours students spend doing homework each night at Air Academy High School. Every fourth student on the school s computer list will be selected to participate in the survey. This should result in a sample size of about 250 students. 6. A car dealer wants to survey its customers a month after their vehicle purchase. The manager of the dealership divides the list of new owners by the type of vehicle they bought (SUV, car, pickup, or minivan) and then randomly calls ten people from each list. 7. Numerical data are often displayed in a(n) or a(n). 8. data are often displayed in a bar graph or circle graph. 9. In a relative frequency histogram, the horizontal axis shows. The vertical axis shows. For 10-12, use the box plot. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 10. Between what two numbers do the middle 50% of the data fall? 11. 25% of the data is greater than what number? 12. 25% of the data is less than what number? 1
13. The table below shows the bushels of corn produced per acre on certain farms in Iowa. Identify: Bushels of Corn Per Acre Farm A 150.4 Farm B 118.4 Farm C 120.6 Farm D 135.7 Farm E 139.1 Farm F 164.3 Farm G 134.2 Farm H 138.1 Farm I 119.5 Farm J 150.0 g) any outliers, show work to justify a) 5 # summary b) mean c) standard deviation d) mode e) range f) interquartile range h) draw a box plot of the data i) Which farms fall within one standard deviation of the mean? j) Which measures of central tendency and variability are best for this data set? Explain! 14. Transfer students to a new high school are sometimes given a standardized test with a mean of 100 and a standard deviation of 20. To two decimal places, convert the raw scores of the following students to z scores: Alice--105 Bob--72 Carol--142 David--133 Elliott--95 15. John weights 220 pounds; his dog Fido weights 90 pounds. If human males weigh an average of 185 pounds with a standard deviation of 20 pounds, and all dogs of Fido's breed have an average weight of 80 pounds with a standard deviation of 5 pounds, how do John and Fido compare, relative to their populations, with respect to weight? 2
Probabilty- Calculator Allowed 16. How many different outfits can you make from 4 shirts, 2 skirts, 2 belts, 3 pairs of socks and one pair of shoes? 17. C 18. 10 2 16 P 6 For 19 25, determine whether one should use a permutation, combination, or the multiplication principle of counting to solve each of the following. Then, solve the problem. 19. Suppose 4 students are entering a vehicle with 4 seats. How many possible seating arrangements are there if any of the students can also be the driver? 20. How many license plates begin with two letters followed by four digits? Assume that no letters or digits are repeated. 21. How many different sundaes can be made by choosing 3 out of 8 toppings at the Sundae Bar to put onto vanilla ice cream? 22. How many ways can you put 5 out of 20 CD s into the CD changer in your car? 23. Your little sister wants to color a picture for you. She has crayons that are: red, blue, yellow, green, black, white and purple. How many set of three crayons can she choose to color the picture? 24. In how many ways can an employer choose five employees from a pool of 12 for five different job assignments? 25. How many distinct arrangements are there for the letters in the word PRINCESSES? For 26 29, find the probability of choosing each type of card at random out of a standard deck of cards. Write your answers as reduced fractions. 26. a Jack 27. not a Diamond 28. an Ace or a Two 29. a black non-face card 30. A spinner is divided into 10 equally sized pieces. Each piece is number with one number from one through ten. What is the probability of obtaining a multiple of four in a single spin? 3
31. Karl attends summer camp each year and he tries a new sport with each visit. This year he decides to take up the sport of archery. When he begins, he just concentrates on holding the bow correctly, lining up the arrow, and getting off a clean shot. At this point, Karl is equally likely to hit any point on the target. a) At this stage, what is the probability that Karl s arrow will hit the bull s eye (assuming it hits the target)? Use the target at the right where the radius of the bull s eye is 6 inches and the radius of the entire target is 18 inches. b) What kind of probability is this? Why? 32. After several days of practice, Karl s aim has improved considerably. Today, Karl hit the bull s eye four out of eleven tries. a) What is the probability today that Karl will hit the bull s eye? b) What kind of probability is this? Why? For 33 36, an experiment consists of selecting a card from an ordinary deck of 52 playing cards, noting what it is, returning it to the deck, reshuffling, then selecting another card and noting its identity as well. A = the event that the card is a spade. B = the event that the card is red. C = the event that the card is a face card. Find each probability. Leave answers as reduced fractions or decimals. 33. P(A and B) 34. P(A or B) 35. P(A and not C) 36. P(not B or C) 37. In a restaurant, a computer randomly assigns a server to one section of tables each day. If there are 5 sections, and only one by the window, what is the probability that George will be assigned the window section at least once in 3 days? 38. A cup manufacturer is contracted by a restaurant to put a scratch off message on the side of 19% of the large drink cups indicating that the purchaser had won a free hamburger. In each of two visits, Marlon purchased a large drink cup. Find the probability that Marlon wins exactly one hamburger. 4
The table below lists the kinds of volunteer work undertaken by students at a high school on Senior Service Day. Suppose a student participating in Senior Service Day is chosen at random. For 39 42, find each probability. 39. P(green team) 40. P(soup kitchen) 41. P(day care blue team) 42. P(red team gardening) Blue Red Green Litter Pickup 40 50 25 30 Gardening 35 45 50 35 Day Care 55 25 35 45 Soup Kitchen 30 35 30 40 Yellow For questions 43-45, a bag contains 5 red marbles, 6 yellow marbles, and 4 green marbles. Two marbles are selected at random, one after the other, without replacement. 43. What is the probability that the first marble is red? 44. What is the probability that the second marble is green given that the first is red. 45. What is the probability that the first marble is red and the second marble is green? 46. A standard deck of cards consists of 52 cards. Suppose two cards are drawn from the deck, but the first card is not replaced before the second card is drawn. Find the probability in each of the following scenarios. a) Both cards are jacks. b) The second card is a red 4 given that first card is an ace. c) Exactly one card is a queen. 5