Quantitative Analysis: Probability question 2

A Nobel Laureate, hosting a lecture for a large audience, is fed up with people who fail to turn their mobile phones off during such events. Based on numerous past performances he knows that the number of phones receiving calls during the lecture is normally distributed with a mean of 2.5 and a variance of 0.25. Before going onstage he tells his associate that if he hears more than 4 phone calls during tonight’s lecture he will stop lecturing forever.

(a) What is the probability that tonight’s lecture will be his last? [Your answer should demonstrate your understanding of the distribution theory underpinning this question – i.e. avoid merely presenting a final figure based solely on an excel calculation]

(b) Assume you only knew the average number of phone calls received during the lecture is 2.5. (You did not know the variance and did not know if the number calls received during lecture is normally distributed). Use another distribution that you learnt to calculate the same probability as in(a).