Question

A Prevention of Domestic Violence hotline receives calls from men, women, and children. An analysis of calls over time indicates that the mean number of calls registered by the hotline is 115.5 per month. ( Assume a month has 30 days. )
a) What is the probability that on a given day fewer than 2 calls would be made to the hotline?
b) During the COVID-19-related quarantine period, the average monthly number of calls to the hotline jumped by 20%. What is the chance that on a given day during the quarantine period, the hotline receives more than 5 calls?

Answer 1

Let X be the number of calls registered by the hotline

X~ Poisson ( = 115.5 per month)

X~ Poisson ( = 115.5/30 per day)

X~ Poisson ( = 3.85 per day)'

a) P( X<2 ) = P( X=0) + P(X=1)

= +

= 0.1032

b)   During quaratine the number of calls to the hotline is ( 1+ 0.2) * 115.5 i.e, 138.6 per month i.e 4.62 per day.

X~ Poisson ( = 4.62 per day)

P ( X>5) = 1- P( X < =5)

= 1- 0.68231

= 0.31769