A-LevelMathematicsProbability and statistics9709/61 · May/June 2020 · Q46 Marks
A fair spinner has five sides numbered 1, 2, 3, 4, 5. The score on one spin is denoted by X. Fiona has another spinner, also with five sides numbered 1, 2, 3, 4, 5. She suspects that it is biased so that the expected score is less than 3. In order to test her suspicion, she plans to spin her spinner 40 times. If the mean score is less than 2.6 she will conclude that her spinner is biased in this way.
- (a)Show that Var(X) = 2.[1]
- (b)Find the probability of a Type I error.[4]
- (c)State what is meant by a Type II error in this context.[1]
Mark scheme
Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.
- [B1] (1²+2²+ 3²+4²+5²) / 5 - 3² (= 2 AG)
- [M1] N(3, 2/40) or N(3, 0.05)
- [M1] (2.6-"3") / √(2/40) (=-1.789)
- [M1] Ф(“-1.789") = 1 – Ф(“1.789")
- [A1] 0.0367 to 0.0368
- [B1] Concluding that spinner is unbiased when it is biased
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