A-LevelMathematicsProbability and statistics9709/61 · Oct/Nov 2020 · Q612 Marks

The time, in minutes, for Anjan's journey to work on Mondays has mean 38.4 and standard deviation 6.9.

(a)Find the probability that Anjan's mean journey time for a random sample of 30 Mondays is between 38 and 40 minutes.[5]
(b)(i)Anjan wishes to test whether his mean journey time is different on Tuesdays. He chooses a random sample of 30 Tuesdays and finds that his mean journey time for these 30 Tuesdays is 40.2 minutes. Assume that the standard deviation for his journey time on Tuesdays is 6.9 minutes. State, with a reason, whether Anjan should use a one-tail or a two-tail test.[1]
(b)(ii)Carry out the test at the 10% significance level.[5]
(b)(iii)Explain whether it was necessary to use the Central Limit theorem in part (b)(ii).[1]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.

[M1] M1 for either correct expression must have √30 (condone continuity correction)
[A1] A1 for ±1.270 or for 1.27 or AWRT
[A1] A1 for ± (-0.3175) must be opposite sign or for 0.317 or 0.318 or AWRT
[M1] For correct method consistent with their values
[A1]
[B1] OE
[B1] Not just 'mean journey time'
[M1] For standardising (must have √30)
[A1]
[M1] For valid comparison (area comparison 0.0765 > 0.05)
[A1 FT] In context. Not definite (e.g. not ‘mean journey time has not changed'). No contradictions. FT their ‘1.429' (Note use of 1-tail test scores B0 M1A1M1(comparison with 1.282) A0 max)
[B1] Allow: Yes, because population distribution not normal.

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