5 A random variable \(X\) has the distribution \(\operatorname { Po } ( 3.2 )\).
- A random value of \(X\) is found.
(a) Find \(\mathrm { P } ( X \geqslant 3 )\).
(b) Find the probability that \(X = 3\) given that \(X \geqslant 3\). - Random samples of 120 values of \(X\) are taken.
(a) Describe fully the distribution of the sample mean.
(b) Find the probability that the mean of a random sample of size 120 is less than 3.3.