A-LevelMathematicsProbability and statistics9709/61 · Oct/Nov 2020 · Q513 Marks

The number of absences per week by workers at a factory has the distribution Po(2.1).

(a)Find the standard deviation of the number of absences per week.[1]
(b)Find the probability that the number of absences in a 2-week period is at least 2.[3]
(c)Find the probability that the number of absences in a 3-week period is more than 4 and less than 8.[2]
(d)Following a change in working conditions, the management wished to test whether the mean number of absences has decreased. They found that, in a randomly chosen 3-week period, there were exactly 2 absences. Carry out the test at the 10% significance level.[5]
(e)State, with a reason, which of the errors, Type I or Type II, might have been made in carrying out the test in part (d).[2]

Mark scheme

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

[B1]
[B1]
[M1] 1 – P(X ≤ 1) any λ, allow one end error.
[A1]
[M1] P(X= 5, 6, 7) any λ, allow one end error.
[A1]
[B1] Accept µ, accept 2.1 (per week)
[M1]
[A1] Accept 0.0499
[M1] For valid comparison. For CV method the comparison can be ‘2 lies in CR of X < 2'
[A1 FT] In context, not definite, e.g. not ‘Mean number of absences has decreased.' No contradictions.
[*B1 FT] H0 rejected OE
[DB1 FT]

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