The ages of prime ministers of Sri Lanka, when they were first sworn to office, are normally distributed with a mean of 58.21 years and a standard deviation of 11.56 years. Find the probability that the age of a randomly selected prime minister of Sri Lanka when he was sworn to office was

(a) less than 50 years,

(b) between 55 and 60 years, and

(c) more than 70 years. 

(d) Identify the unusual events in parts (a)–(c). Explain your reasoning.

Find the indicated probabilities. If convenient, use technology to find the probabilities.