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.

$$n = 40 \quad \Sigma t = 560 \quad \Sigma t ^ { 2 } = 7850$$

(a) 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 $\mathrm { N } ( 14.2,0.3 )$.\\
(b) 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.\\

\hfill \mbox{\textit{CAIE S2 2021 Q6}}