Question

4. Deaths in a small city occur at a rate of 5 per week and are known to follow a Poisson distribution.

a. What is the expected number of deaths in a 3-day period?

b. What is the probability no one dies in a 3-day period?

c. What is the probability that at least 250 people die in 52 weeks?

d. What is the probability that number of deaths in a 3-day period is less than µ + σ?

Answer 1

a) expected number of deaths in a 3-day period =3*5/7=2.14

b)  probability no one dies in a 3-day period =P(X=0)=e^-2.14*2.14⁰/0! =0.1173 ( please try 0.1177 if this comes wrong due to rounding error)

c)

expected number of death in 52 weeks =52/5=260

and std deviaiton =sqrt(260)=16.1245

frm normal approximation and continuity correction:

probability that at least 250 people die in 52 weeks:

P(X>=250)=1-P(X<=249)=1-P(Z<(249.5-260)/16.1245)=1-P(Z<-0.65)=1-0.2578 =0.7422

d)

here mean µ =2.14

and std deviaiton  σ =sqrt(2.14)=1.46

hence P(X<µ + σ)=P(X<2.14+1.46)=P(X<3.60)=P(X<=3)= =0.8310 (please try 0.8305 if this comes wrng and revert)