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.

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]