| Date | None Specimen | Marks available | 5 | Reference code | SPNone.3sp.hl.TZ0.3 |
| Level | HL only | Paper | Paper 3 Statistics and probability | Time zone | TZ0 |
| Command term | Find | Question number | 3 | Adapted from | N/A |
Question
The weights of adult monkeys of a certain species are known to be normally distributed, the males with mean 30 kg and standard deviation 3 kg and the females with mean 20 kg and standard deviation 2.5 kg.
Find the probability that the weight of a randomly selected male is more than twice the weight of a randomly selected female.
Two males and five females stand together on a weighing machine. Find the probability that their total weight is less than 175 kg.
Markscheme
we are given that \(M \sim {\text{N(30, 9)}}\) and \(F \sim {\text{N(20, 6.25)}}\)
let \(X = M - 2F;{\text{ }}X \sim {\text{N}}\)(\( - 10\), \(34\)) M1A1A1
we require \({\text{P}}(X > 0)\) (M1)
= 0.0432 A1
[5 marks]
let \(Y = {M_1} + {M_2} + {F_1} + {F_2} + {F_3} + {F_4} + {F_5};{\text{ }}Y \sim {\text{N(160, 49.25)}}\) M1A1A1
we require \({\text{P}}(Y < 175) = 0.984\) A1
[4 marks]
