Mathematics 9709 · AS & A Level · Continuous random variables
Continuous random variables — practice question
An athlete's quickest time in a 400 m race is known as their personal best (PB). The PBs of the athletes in a large athletics club are normally distributed, with a mean of 49.2 seconds and a standard deviation of 2.8 seconds.
(i)[4]
Determine the probability that a randomly selected athlete in this club has a PB between 46 and 53 seconds.
(ii)[3]
It is given that 92% of the athletes in this club have PBs greater than $t$ seconds. Determine the value of $t$.
(iii)[3]
Three athletes are picked at random from the club. Find the probability that exactly 2 have PBs below 46 seconds.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Standardise accurately to give $P\!\left(\dfrac{46-49.2}{2.8}<Z<\dfrac{53-49.2}{2.8}\right)$.” …