Pearson Edexcel A level Mathematics Statistics & Mechanics Year 2 Textbook + ebook (A level Maths and Further Maths 2017)
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Pearson Edexcel A level Mathematics Statistics & Mechanics Year 2 Textbook + ebook (A level Maths and Further Maths 2017)
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b Let Y be the number of adults who classify as ‘genius’. Y ~ B(20, 0.00383) P(Y ù 2) = 1 − P(Y < 1) = 1 − 0.9973379… = 0.00266 (3 s.f.)
The outcome of one event can affect the probability for another event. If a football team scores a goal, the probability that they will win the match will increase. → Mixed exercise Q8 A box of 24 chocolates contains 10 dark and 14 milk chocolates. Linda chooses a chocolate at random and eats it, followed by another one. a Draw a tree diagram to represent this information. Find the probability that Linda eats: b two dark chocolates c one dark and one milk chocolate d two dark chocolates given that she eats at least one dark chocolate. P A school has 75 students in year 12. Of these students, 25 study only humanities subjects (H ) and 37 study only science subjects (S ). 11 students study both science and humanities subjects. a Draw a twoway table to show this information. b Find: i P(S9 ∩ H9) ii P(S H ) iii P(H S9) 21 M02_EDSM2_SB_AL_83282_U02_016036.indd 21
Unit Tests
A bag contains five red and four blue tokens. A token is chosen at random, the colour recorded and the token is not replaced. A second token is chosen and the colour recorded. a Draw a tree diagram to illustrate this situation. Find the probability that: b the second token is red given that the first token is blue 31 M02_EDSM2_SB_AL_83282_U02_016036.indd 31
The weights of a group of dormice, D grams, are modelled as D ~ N(µ, 25). If 97.5% of dormice weigh less than 70 grams, find µ. By calculating the product moment correlation coefficient for these data, test at the 5% level of significance whether there is evidence to support the meteorologist’s claim. State your hypotheses clearly. (4 marks) 14 M01_EDSM2_SB_AL_83282_U01_001015.indd 14 The data are coded using x = log w and y = log m. a Copy and complete the table showing the values of log w and log m. b Calculate the product moment correlation coefficient for the coded data. b Find the probability that on a randomly chosen day, i Bill travels by train and is late ii Bill is late. The masses, X grams, of a large population of squirrels are modelled as a normal distribution with X ~ N(480, 402). a Find the probability that a squirrel chosen at random has a mass greater than 490 g.(1 mark) A naturalist takes a random sample of 30 squirrels from the population. b Find the probability that at least 15 of the squirrels have a mass between 470 g and 490 g. (4 marks) r measures linear correlation. The closer r is to 1 or −1, the more closely a linear regression model will fit the data.
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