Hint
Check both expected success and failure counts. Use the binomial mean.
Worked solution
(a)
\(\displaystyle np=\frac{162}{5}\)
Answer: \(\displaystyle \frac{162}{5}\).
Answer: \(\displaystyle \frac{162}{5}\)
(b)
\(\displaystyle np(1-p)=\frac{567}{25}\)
Answer: \(\displaystyle \frac{567}{25}\).
Answer: \(\displaystyle \frac{567}{25}\)
(c)
\(P(Y<34.5)=\Phi(0.440958552)=0.670378498153685\)
Answer: \(0.670378498153685\).
Answer: \(\approx 0.670378498153685\)
Maths4U indicative marking guidance
Maths4U indicative marking guidance, not an official mark scheme. Credit valid alternative reasoning and consequential working; do not award a reasoning mark for an unexplained final answer.
(a) · 2 marks
- 1 mark: Use the binomial mean.
- 1 mark: Obtain the stated result with the required sign, units and domain.
Alternative methods: Any complete mathematically valid method with the stated assumptions and equivalent result is acceptable.
Common error: Do not apply a continuity correction to an already continuous normal variable.
(b) · 2 marks
- 1 mark: Use the binomial variance.
- 1 mark: Obtain the stated result with the required sign, units and domain.
Alternative methods: Any complete mathematically valid method with the stated assumptions and equivalent result is acceptable.
Common error: At least k uses k−0.5, not k+0.5.
(c) · 2 marks
- 1 mark: Apply k+0.5 before standardising.
- 1 mark: Obtain the stated result with the required sign, units and domain.
Alternative methods: Any complete mathematically valid method with the stated assumptions and equivalent result is acceptable.
Common error: Do not apply a continuity correction to an already continuous normal variable.
Total: 6 marks.