Pearson Edexcel Level 3 GCE Mathematics Advanced Subsidiary Paper 21: Statistics. October 2020 8MA0/21 Question Paper and Mark Scheme.

Mathematics Advanced Subsidiary Paper 21: Statistics Afternoon Paper Reference 8MA0/21 Wednesday 14 October 2020 Pearson Edexcel Level 3 GCE 2 5 10 15 20 25 Time (minutes) 0 Frequency density 0 Figure 1 ...

Mathematics Advanced Subsidiary Paper 21: Statistics Afternoon Paper Reference 8MA0/21 Wednesday 14 October 2020 Pearson Edexcel Level 3 GCE 2 5 10 15 20 25 Time (minutes) 0 Frequency density 0 Figure 1 The histogram in Figure 1 shows the times taken to complete a crossword by a random sample of students. The number of students who completed the crossword in more than 15 minutes is 78 Estimate the percentage of students who took less than 11 minutes to complete the crossword. (4) 2. Jerry is studying visibility for Camborne using the large data set June 1987. The table below contains two extracts from the large data set. It shows the daily maximum relative humidity and the daily mean visibility. Date Daily Maximum Relative Humidity Daily Mean Visibility Units % 10/06/1987 90 5300 28/06/1987 100 0 (The units for Daily Mean Visibility are deliberately omitted.) Given that daily mean visibility is given to the nearest 100, (a) write down the range of distances in metres that corresponds to the recorded value 0 for the daily mean visibility. (1) Jerry drew the following scatter diagram, Figure 2, and calculated some statistics using the June 1987 data for Camborne from the large data set. 80 85 90 95 100 5000 4000 3000 2000 1000 Daily maximum relative humidity Daily mean visibility Q1 IQR Daily mean visibility 1100 1600 Daily maximum relative humidity (%) 92 8 Figure 2 Jerry defines an outlier as a value that is more than 1.5 times the interquartile range above Q3 or more than 1.5 times the interquartile range below Q1. (b) Show that the point circled on the scatter diagram is an outlier for visibility. (2) (c) Interpret the correlation between the daily mean visibility and the daily maximum relative humidity. (1) 5 Jerry drew the following scatter diagram, Figure 3, using the June 1987 data for Camborne from the large data set, but forgot to label the x–axis. 2 4 6 8 10 12 14 5000 4000 3000 2000 1000 Daily mean visibility O Figure 3 (d) Using your knowledge of the large data set, suggest which variable the x-axis on this scatter diagram represents. (1) Question 2 continued 3. In a game, a player can score 0, 1, 2, 3 or 4 points each time the game is played. The random variable S, representing the player’s score, has the following probability distribution where a, b and c are constants. s 0 1 2 3 4 P(S = s) a b c 0.1 0.15 The probability of scoring less than 2 points is twice the probability of scoring at least 2 points. Each game played is independent of previous games played. John plays the game twice and adds the two scores together to get a total. Calculate the probability that the total is 6 points. (6) 4. A lake contains three different types of carp. There are an estimated 450 mirror carp, 300 leather carp and 850 common carp. Tim wishes to investigate the health of the fish in the lake. He decides to take a sample of 160 fish. (a) Give a reason why stratified random sampling cannot be used. (1) (b) Explain how a sample of size 160 could be taken to ensure that the estimated populations of each type of carp are fairly represented. You should state the name of the sampling method used. (2) As part of the health check, Tim weighed the fish. His results are given in the table below. Weight (wkg) Frequency (f) Midpoint (mkg) 2  w < 3.5 8 2.75 3.5  w < 4 32 3.75 4  w < 4.5 64 4.25 4.5  w < 5 40 4.75 5  w < 6 16 5.5 ( ) You may use fm m ¬ ¬ 692 and f 2 3053 (c) Calculate an estimate for the standard deviation of the weight of the carp. (2) Tim realised that he had transposed the figures for 2 of the weights of the fish. He had recorded in the table 2.3 instead of 3.2 and 4.6 instead of 6.4 (d) Without calculating a new estimate for the standard deviation, state what effect (i) using the correct figure of 3.2 instead of 2.3 (ii) using the correct figure of 6.4 instead of 4.6 would have on your estimated standard deviation. Give a reason for each of your answers. (2) 5. Afrika works in a call centre. She assumes that calls are independent and knows, from past experience, that on each sales call that she makes there is a probability of 1 6 that it is successful. Afrika makes 9 sales calls. (a) Calculate the probability that at least 3 of these sales calls will be successful. (2) The probability of Afrika making a successful sales call is the same each day. Afrika makes 9 sales calls on each of 5 different days. (b) Calculate the probability that at least 3 of the sales calls will be successful on exactly 1 of these days. (2) Rowan works in the same call centre as Afrika and believes he is a more successful salesperson. To check Rowan’s belief, Afrika monitors the next 35 sales calls Rowan makes and finds that 11 of the sales calls are successful. (c) Stating your hypotheses clearly test, at the 5% level of significance, whether or not there is evidence to support Rowan’s belief. (4)