1 Dimitra is an athlete who competes in 400 m races. The times, in seconds, for her first six races of the 2012 season were
$$\begin{array} { l l l l l l }
54.86 & 53.09 & 53.75 & 52.88 & 51.97 & 51.81
\end{array}$$
- Assuming that these data form a random sample from a normal distribution, construct a \(95 \%\) confidence interval for the mean time of Dimitra's races in the 2012 season, giving the limits to two decimal places.
- For the 2011 season, Dimitra's mean time for her races was 53.41 seconds. After her first six races of the 2012 season, her coach claimed that the data showed that she would be more successful in races during the 2012 season than during the 2011 season. Make two comments about the coach's claim.