7 The continuous random variable \(T\) is equally likely to take any value from 5.0 to 11.0 inclusive.
- Sketch the graph of the probability density function of \(T\).
- Write down the value of \(\mathrm { E } ( T )\) and find by integration the value of \(\operatorname { Var } ( T )\).
- A random sample of 48 observations of \(T\) is obtained. Find the approximate probability that the mean of the sample is greater than 8.3, and explain why the answer is an approximation.