Quantitative Analysis: Probability question

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).