Year 9 Unit G Revision. Exercise A

Transcription

1 Year 9 Unit G Revision Exercise A 1.) Find the mode, median, mean, range and interquartile range of each of the following lists. a.) 11, 13, 13, 16, 16, 17, 19, 20, 24, 24, 24, 25, 30 b.) 21, 36, 78, 45, 12, 19, 18, 17, 56, 60 2.) Draw a box- plot for the data in Question 1b. 3.) The table below shows the number of legs that various chickens caught locally had. Number of legs Frequency a.) Find the modal number of legs. b.) Find the median number of legs c.) Find the mean number of legs. d.) Find the range of the number of legs. 4.) The table below shows the distribution of the weight of some frogs. Weight (w g) 0 < w < w < w < w < w < w < w 250 Frequency a.) Calculate an estimate of the mean weight of the frogs. b.) Draw a cumulative frequency curve for the weight of the frogs. c.) Use your graph to calculate the median and interquartile range of the weight of the frogs. d.) Use your graph to estimate percentage of frogs that weighed more that 110g. 5.) The table below shows the time that it took a group of Year 9 students to annoy Mr. K from the start of the lesson. Time (t secs) 0 < t 5 5 < t < t < t < t < t < w 90 Frequency a.) Use the data given to calculate an estimate of the mean time. d.) From your histogram estimate the number of people who took between 15 and 25 seconds to annoy Mr. K. 6.) The table below shows the number of times that a frog cried each day over the course of 50 days. Number of times Frequency For the data given in the table, find the mean, median, mode and range.

2 7.) The boxplots below show the salaries of law and business graduates from a particular university. Annual salary (US dollars, thousands) a.) Write a sentence comparing the median values of business and law graduates. b.) Find the interquartile range for both business and law graduates. 8.) The cumulative frequency curve below shows the marks achieved by students in a French test. a.) How many students sat the test? b.) Estimate the median mark in the test. c.) The French teacher decided that 80% of those who sat the test should pass the test. What does this mean the pass mark for the test should be?

3 10.) For the following set of data, find: (a.) the mode, (b.) the median, (c.) mean, (d.) range, (e.) interquartile range. 8, 10, 7, 6, 13, 14, 7, 5, 8, 9, 10, 7, 3, 19, 23, 6, 6, 8, 7, 9, 28, 19, 20, 4 f.) Draw the box- plot for this set of data. 11.) The box- plot below shows the amount of time taken to complete a simple test question by 200 students. a.) Write the median time. b.) What was the shortest time taken? c.) Approximately how many students took at least 60 seconds? 12.) For the data given in both tables below, find the (i.) mean, (ii.) mode, (ii.) median, and (iii.) range of the data. (a.) Number of eggs Number of hens (b.) Number of iggs Frequency ) Calculate an estimate of the mean for each of the following. (a.) Height (h cm) Number of students 50 < h 100 < h 120 < h 140 < h 150 < h 170 < h (b.) Time (t secs) 10 t < t < t < t < t < t < t < 80 Frequency t < ) The table below shows the weights of a group of kangaroos. Mass (m kg) 0 < m 5 5 < m < m < m < m 25 Frequency a.) Draw a cumulative frequency curve for this set of data. b.) Use your graph to find the median and the interquartile range of the data. c.) Use your graph to determine what percentage of kangaroos weigh more than 17.5kg.

4 Exercise B 1.) A bag contains 7 yellow and 3 green cats. One cat is picked at random. a.) What is the probability that the cat chosen is yellow? b.) What is the probability that the cat chosen is green? 2.) Two four- sided dice are thrown. a.) Draw a possibility space to show all the possible outcomes of the two dice. b.) What is the probability that both dice are rolled onto the same number? 3.) The probability that a dry cleaner has more than 100 customers during any one day is 0.6 a.) Copy and complete the tree diagram below to show all the possible outcomes for two days. b.) Find the probability that there are more than 100 customers on: (i) both days (ii) only one day 4.) The probability of Juliana annoying her Maths teacher in a lesson are 0.05 (a.) What is the probability that Juliana will not annoy her Maths teacher in a lesson? (b.) Over the course of 300 lessons, how many times would you expect Juliana to annoy her Maths teacher? 5.) Juan Carlos rolls a coloured dice twice. Two of the faces are red, and the other four are blue. (a.) Copy and complete the tree diagram. (b.) Find the probability that Juan Carols gets: (i) two reds (ii) two blues (iii) different colours 6.) A mother has an equal chance of giving birth to either a boy or a girl. Jimena plans to have two children. What is the probability that they will both be girls? 7.) Nine cards each have one letter written on them. The letters are C, O, O, L, B, E, A, N, Z. Catalina picks a card at random. What is the probability that the card is a vowel?

5 8.) A bag contains 7 yellow and 3 green discs. A disc is pulled out at random, its colour noted, and then the disc is returned to the bag. A second disc is then pulled out random and its colour noted. a.) Draw a probability tree to show all the possible outcomes. b.) Use the tree to calculate the probability that: (i) both discs are yellow (ii) the second disc is green 9.) The mighty soccer team of Saprissa have a probability of 0.67 of winning a game, and a probability of 0.14 of losing a game. What is the probability of Saprissa drawing a game? 10.) A spinner has 5 equal sectors, two of which are red, one is yellow and two are green. The spinner is spun three times. (a.) Copy and complete the tree diagram below to show all the possible outcomes and probabilities. (b.) Find the probability that all spins are red. (c.) Find the probability that at least two of the spins are red. 11.) María Jesús has 20 cards in her hand that are numbered from 1 to 20. She picks one card at random. What is the probability the card is: a.) an even number b.) a number less than 10 c.) a prime number d.) a multiple of 3 12.) A bag contains 4 blue and 3 red balls. Two balls are picked out of the bag without replacement. a.) Draw a tree diagram to show all the possible outcomes. b.) Use your tree diagram to find the probability that the two balls are: (i) the same colour (ii) different colours 13.) Thalia likes to go swimming. The probability that she will go swimming on any day is If Thalia goes swimming then the probability that she will have a huge ice- cream is 0.45, otherwise the probability is only a.) Draw a tree diagram to show all the possible outcomes. b.) What is the probability that: (i) Thalia will go swimming and she will not have a huge ice- cream. (ii) Thalia will have a huge ice- cream.

6 14.) In a packet of M&M s Ignacio discovers that there are only three colours red, green and yellow in the ratio 5 : 4 : 2. (a.) If Ignacio picks out a M&M at random, what is the probability that the M&M will be yellow? (b.) If Ignacio does pick out a yellow M&M and then eats it, will the probability of picking out a yellow M&M now change? Explain your answer. 15.) George the cat is determined to pass his driving test. Every time he takes the test he estimates that he has a 2 5 probability of passing. He only has enough money to take the test four times. If he passes the test he won t take it again. What is the probability that George will pass his test at some point during his maximum of 4 tests?