7 A club secretary collects data about the time, \(T\) minutes, needed to process the details of a new member. The mean of \(T\) is denoted by \(\mu\). The variance of \(T\) is denoted by \(\sigma ^ { 2 }\). The results of a random sample of 40 observations of \(T\) are summarised as follows.
\(\mathrm { n } = 40 \quad \Sigma \mathrm { t } = 396.0 \quad \Sigma \mathrm { t } ^ { 2 } = 4271.40\)

1. Determine a 99\% confidence interval for \(\mu\).
2. The secretary discovers that over a long period the value of \(\sigma ^ { 2 }\) is in fact 10.0 . The secretary collects an independent random sample of 50 observations of \(T\) and constructs a new 99\% confidence interval for \(\mu\) based on this sample of size 50 , but using \(\sigma ^ { 2 } = 10.0\). Find the probability that this new confidence interval contains the value \(\mu + 1.6\).