6 The random variable \(T\) denotes the time, in seconds, for 100 m races run by Tania. \(T\) is normally distributed with mean \(\mu\) and variance \(\sigma ^ { 2 }\). A random sample of 40 races run by Tania gave the following results.
$$n = 40 \quad \Sigma t = 560 \quad \Sigma t ^ { 2 } = 7850$$
- Calculate unbiased estimates of \(\mu\) and \(\sigma ^ { 2 }\).
The random variable \(S\) denotes the time, in seconds, for 100 m races run by Suki. \(S\) has the independent distribution \(\mathrm { N } ( 14.2,0.3 )\). - Using your answers to part (a), find the probability that, in a randomly chosen 100 m race, Suki's time will be at least 0.1 s more than Tania's time.