OCR 2023 GCE FURTHER MATHEMATICS B MEI Y432/01: STATISTICS MINOR A LEVEL QUESTION PAPER & MARK SCHEME (MERGED)

A fair spinner has ten sectors, labelled 1, 2, …, 10. In order to start a game, Kofi has to obtain an 8, 9 or 10 on the spinner. (a) Find the probability that Kofi starts the game on the third spin. [2] (b) Find the probability that Kofi takes at least 5 spins to start the game. [1] (c) Determine the probability that the number of spins required to start the game is within 1 standard deviation of its mean. [5] 2 A company manufactures batches of twenty thousand tins which are subsequently filled with fruit. The company tests tins from each batch to make sure that they are strong enough. The test is easy and cheap to carry out, but when a tin has been tested it is no longer suitable for filling with fruit. (a) (i) Explain why a sample size of 5 tins per batch may not be appropriate in this case. [1] (ii) Explain why a sample size of 1000 tins per batch may not be appropriate in this case. [1] The company tests a sample of 30 tins from each batch. (b) Explain why it would not be sensible for the sample to consist of the final 30 tins produced in a batch. [1] (c) Give two features that the sample should have. [2] 3 © OCR 2023 Y432/01 Jun23 Turn over 32 3 A fair four-sided dice has its faces numbered 0, 1, 2, 3. The dice is rolled three times. The discrete random variable X is the sum of the lowest and highest scores obtained. (a) Show that P(X = 1) = 3 .