Stephanie gets an average of 11 calls during her 8 hour work day. What is the probability that Stephanie will get more than 4 calls in a 2 hour portion of her work day

0.145

Step-by-step explanation:

Suppose λ = average number of an event occurring in an interval of a presented  length; &

x =  no. of events occurring in an interval length t

Thus, x has a Poisson distribution with parameter λt.

i.e.

Given that:

The average number of call every 8 hours = 11

Then, the parameter for the Poisson process

where;

t = 2 hours

Also,

x = no. of calls occurring at an interval of length 2

The required probability is as follows:

P(x > 4) = 1 - [P ( x≤ 4) ]

= 1 - [13.38037]× 0.06393

= 1 - 0.855407

= 0.14459

≅ 0.145    ( to  3 decimal place)

the answer is a and d