Question

Problem 1 A large office complex has many employees, each with a workstation. Despite the IT department’s repeated warnings, several workstations are infected with a virus or some other security compromise each workday. The IT department figures an average of 25 infections per day. Use a Poisson distribution as a model for the number of infections during a workday, and assume one day’s infections have no impact on another day’s infections (the employees never learn). Estimate the chance that more than 700 infections occur during one month (30 days).

Answer 1

here as we know mean of poisson distribution $\lambda$ =25

and std deviaiton =( $\lambda$ )^1/2 =5

for 30 days expected number of infections =30*25=750

and std deviaiton =5*(30)^1/2 =27.386

for normal distribution z score =(X- $\mu$ )/ $\sigma$ x
here mean=       $\mu$ =	750
std deviation   = $\sigma$ =	27.386

hence from normal approximation and continuity correction:

chance that more than 700 infections occur during one month:

probability =

P(X>700.5)

=

P(Z>-1.81)=

1-P(Z<-1.81)=

1-0.0351=

0.9649