PROBABILITY & STATISTICS TEST Name: 1. June suspects that a dice may be biased. To test her suspicions, she rolls the dice 6 times and rolls 6, 6, 4, 2, 6, 6. She concludes that the dice is biased because she expected to get only one 6. Do you agree with June's conclusion? Briefly justify your answer. 2. In a school of 1500 high school students, a random survey is conducted into the preferred sport of high school students. The results are given below: (2, 1) Sport # of Votes Soccer 45 Basketball 30 Rugby 23 Track and Field 17 Other 15 a) If a high school student is selected at random, estimate the probability that this student prefers either Rugby or Track and Field. b) Briefly explain why your answer is only an estimate of the probability. 3. Brenda rolls one red die and one blue die. a) Draw a grid showing the possible outcomes. b) What is the probability that the number shown on the red die will be higher than the number shown on the blue die?
4. A coin is tossed 3 times. What is the probability that the result will be two heads and one tails? 5. Of 45 students that went to summer camp, 29 participated in the sailing activity (S), 22 participated in the table tennis competition (T), and 6 did neither of these two activities. 7 marks (2, 1, 1, 1, 1, 1) a) Draw a Venn diagram to represent this information: b) Determine the probability that a randomly selected student participated in (i) Sailing. (ii) Both activities. (iii) Table tennis, but not sailing. (iv) Sailing, given that the student participated in at least one activity. (v) Table tennis, given that the student did not go sailing. 6. Five cards are marked with the numbers 1, 2, 3, 4, 5. A card is randomly selected, its number is noted, it is replaced and a 2 nd card is selected. What is the probability that 4 marks (1, 1, 2) a) Both cards are even numbers? b) Both cards are odd numbers? c) There is one even and one odd numbered card?
7. Marla has a bag of chocolates. There are 5 plain chocolates, 7 that contain nuts and 2 that contain raisins. Marla selects a chocolate at random, eats it, then selects a 2nd chocolate which she also eats. What is the probability that 6 marks (2, 2, 2) a) The first chocolate is plain and the 2nd chocolate contains nuts? b) She selects two plain chocolates? c) At least one of the chocolates contains raisins? 8. Travel times, in minutes, to ISM on a weekday morning are given below: 12, 20, 15, 6, 18, 17, 19, 18, 45, 10, 14 6 marks (2, 1, 1, 2) a) Construct a stem-and-leaf plot for the data. b) Find the median. c) Find the mean. d) Find the interquartile range. 9. The following table represents the scores obtained when a die was rolled. The mean score is 3.5. Find the value of k. Score 1 2 3 4 5 6 Frequency 8 k 11 10 7 10
Frequency (number of students) 10. 21 students are surveyed about how many hours of sleep they get each night. The results are shown in the frequency table below. Hours of Sleep Number of Students (x) (f) 4 2 5 5 6 4 7 3 8 4 10 2 12 1 Cumulative frequency a) Complete the cumulative frequency column. b) Determine the median. 30 f 11. Students who live between 15 and 30 km from school are asked how many minutes they spend traveling to school. The results of the survey are shown in this histogram: 20 10 10 20 30 40 50 60 70 80 90 100 Time in minutes x New data is collected from additional students who live between 0 and 2 km from school. This new data is added to the survey results. a) Briefly describe the effect of the new data on the mean and median of the survey. b) Briefly describe the effect of the new data on the range of the survey.
Number of students 12. The cumulative frequency graph below has been drawn from a frequency table showing the time it takes a number of students to complete a computer game. 7 marks (1, 1, 2, 1, 2) a) How many students took 15 minutes or less to complete the game? f 200 180 160 140 b) Estimate the median time taken to complete the game. 120 100 80 60 c) The middle 50% of times lie between a minutes and b minutes, where a < b. Write down the values of a and b. 40 20 0 5 10 15 20 25 30 35 40 45 50 55 60 Time in minutes d) How many students took longer than 50 minutes? e) Draw a box-and-whisker plot to represent the data shown in the cumulative frequency graph. 13. The box-and-whisker plots shown here represent the 800-meter running times from two grade 10 classes. (1, 2) a) Which class would have the higher mean? b) Explain how the distributions differ. Be specific.
14. Consider the set of scores: 3, 0, 7, 2, 8, 3, 11, a, b. The mean of the scores is 5, the median of the scores is 4, and a < b. Find a and b. 15. Match each histogram to its corresponding box-and-whisker plot: A B C D