(a)[3]
Calculate unbiased estimates for $\mu$ and $\sigma^2$.
(b)[5]
Using your answers to part (a), determine the probability that, in one randomly selected 100 m race, Suki’s time is at least $0.1\text{ s}$ longer than Tania’s time.
Mathematics 9709 · AS & A Level · Sampling and estimation
Sampling and estimation — practice question
The random variable $T$ represents Tania’s 100 m race times, measured in seconds. It follows a normal distribution with mean $\mu$ and variance $\sigma^2$. A random sample of $40$ of Tania’s races produced the following values: $n = 40$, $\sum t = 560$, $\sum t^2 = 7850$.