11 The discrete random variable \(X\) has a uniform distribution over the set of all integers between 25 and \(n\) inclusive, where \(n\) is a positive integer with \(n > 25\).
- Determine \(\mathrm { P } \left( \mathrm { X } < \frac { \mathrm { n } + 25 } { 2 } \right)\) in each of the following cases.
- \(n\) is even
- \(n\) is odd
- Determine an expression in terms of \(n\) for the variance of the mean of 100 independent values of \(X\).
- Given that \(n = 75\), calculate an estimate of the probability that the mean of 100 independent values of \(X\) is less than 48 .