5. The time taken in minutes, \(T\), for a mechanic to service a bicycle follows a normal distribution with a mean of 25 minutes and a variance of 16 minutes \(^ { 2 }\).
Find
- \(\mathrm { P } ( T < 28 )\),
- \(\quad \mathrm { P } ( | T - 25 | < 5 )\).
One afternoon the mechanic has 3 bicycles to service.
- Find the probability that he will take less than 23 minutes on each of the three bicycles.
(4 marks)