Mathematics 9709 · AS & A Level · Sampling and estimation
Sampling and estimation — practice question
The random variable $T$ represents the time, in seconds, for 100 m races completed by Tania. $T$ follows a normal distribution with mean $\mu$ and variance $\sigma^2$. A random sample of 40 races run by Tania produced the following data: $n = 40$, $\sum t = 560$, $\sum t^2 = 7850$.
(a)[3]
Calculate the unbiased estimates for $\mu$ and $\sigma^2$.
(b)[5]
The random variable $S$ represents the time, in seconds, for 100 m races run by Suki. $S$ has the independent distribution $N(14.2, 0.3)$. Using your answers to part (a), find the probability that, in a randomly selected 100 m race, Suki’s time will be at least $0.1\text{ s}$ more than Tania’s time.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Identifies the estimate of the mean as $\mu = 14$” …