The number of accidents per 3-month period on a certain road has the distribution Po(λ). In the past the value of λ has been 5.7. Following some changes to the road, the council carries out a hypothesis test to determine whether the value of λ has decreased. If there are fewer than 3 accidents in a randomly chosen 3-month period, the council will conclude that the value of λ has decreased.

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2023). The mark or mark type is shown in brackets.

1. [M1] e^-5.7(1 + 5.7 + 5.7^2/2!) or e^-5.7(1 + 5.7 + 16.245) or 0.003346 + 0.01907 + 0.05436
2. [M1] Allow one end error. Must see this expression.
3. [A1] = 0.0768 (3 sf)
4. [A1] SC B1 for unsupported answer of 0.0768 .
5. [M1] e^-0.9(1+0.9+0.9^2/2!)
6. [M1] Attempted; allow one end error (must see expression).
7. [A1] = 1 - e^-0.9(1+0.9 + 0.9^2/2!) = 1 − e^-0.9(1 + 0.9 + 0.405) = 1 – (0.4066 + 0.3659 + 0.1647)
8. [A1] Correct expression P(X ≥ 3) no end errors (must see expression).
9. [A1] = 0.0629 (3 sf)
10. [A1] SC B2 for unsupported answer of 0.0629 .