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1、目录Section A1Representation of data .Measures of location. Measures of spreadSection B9ProbabilitySection C14Permutations and combinationsSection D19Probability distributionsExpectation and Variance of a random VariableSection E22The binomial distributionSection F26The normal distributionAnswer30Sect
2、ion A30Section B36Section C39Section D40Section E42Section F44Section A Representation of data Measures of location Measures of spread1 The weights in kilograms of two groups of 17-year-old males from country P and country Q are displayed in the following back-to-back stem-and-leaf diagram. In the t
3、hird row of the diagram,. . . 4 | 7| 1 . . . denotes weights of 74 kg for a male in country P and 71kg for a male in country Q.(02w) (i) Find the median and quartile weights for country Q. 3(ii) You are given that the lower quartile, median and upper quartile for country P are 84, 94 and 98 kg respe
4、ctively. On a single diagram on graph paper, draw two box-and-whisker plots of the data. 4(iii) Make two comments on the weights of the two groups. 22 (i) (03s) The diagram represents the sales of Superclene toothpaste over the last few years. Give a reason why it is misleading. 1(ii) The following
5、data represent the daily ticket sales at a small theatre during three weeks.52, 73, 34, 85, 62, 79, 89, 50, 45, 83, 84, 91, 85, 84, 87, 44, 86, 41, 35, 73, 86.(a) Construct a stem-and-leaf diagram to illustrate the data. 3(b) Use your diagram to find the median of the data. 13 A random sample of 97
6、people who own mobile phones was used to collect data on the amount of time they spent per day on their phones. The results are displayed in the table below. (03s)Time spent per day(t minutes)0 t 55 t 1010t 2020t 3030t 4040 t 70Numberof people 11 20 32 18 10 6(i) Calculate estimates of the mean and
7、standard deviation of the time spent per day on these mobile phones. 5(ii) On graph paper, draw a fully labelled histogram to represent the data. 44 A computer can generate random numbers which are either 0 or 2. On a particular occasion, it generates a set of numbers which consists of 23 zeros and
8、17 twos. Find the mean and variance of this set of 40 numbers. 4 (03w)5 The floor areas, x m2, of 20 factories are as follows. (03w)150 350 450 578 595 644 722 798 802 9041000 1330 1533 1561 1778 1960 2167 2330 2433 3231Represent these data by a histogram on graph paper, using intervals0 x 500, 500
9、x 1000, 1000 x 2000, 2000 x 3000, 3000 x 4000. 46 Two cricket teams kept records of the number of runs scored by their teams in 8 matches. The scores are shown in the following table. (04s)Team A150 220 77 30 298 118 160 57Team B166 142 170 93 111 130 148 86(i) Find the mean and standard deviation o
10、f the scores for team A. 2The mean and standard deviation for team B are 130.75 and 29.63 respectively.(ii) State with a reason which team has the more consistent scores. 27 In a recent survey, 640 people were asked about the length of time each week that they spent watching television. The median t
11、ime was found to be 20 hours, and the lower and upper quartiles were 15 hours and 35 hours respectively. The least amount of time that anyone spent was 3 hours, and the greatestamount was 60 hours. (04s)(i) On graph paper, show these results using a fully labelled cumulative frequency graph. 3(ii) U
12、se your graph to estimate how many people watched more than 50 hours of television each week. 28 The lengths of cars travelling on a car ferry are noted. The data are summarised in the following table. (04w) Length of car (x metres)FrequencyFrequency density2.80 x 3.0017853.00 x 3.10242403.10 x 3.20
13、191903.20 x 3.408a9 The ages, x years, of 18 people attending an evening class are summarised by the following totals: x = 745, x2 = 33 951. (04w)(i) Calculate the mean and standard deviation of the ages of this group of people. 3(ii) One person leaves the group and the mean age of the remaining 17 people is exactly 41 years. Find the age of the person who left and the standard deviation of the ages of the remaining 17 people. 410 The following table shows th
