business statistics

Question

Suppose that a Covid-19 testing centre receives two phones calls, on average, per minute concerning test results. Required:

a) What are the conditions for this experiment to be considered a Poisson experiment? Motivate. (4)

b) What is the expected number of phone calls regarding test results per hour? (2)

c) What is the probability that more zero but less than four phone calls regarding test results are received in any given period of two minutes? (9)

d) What is the probability that more than one phone calls regarding test results are received in any given period of three minutes? (7)

e) What is the probability that no phone calls regarding test results are received in any given period of one minute?

Answer 1

a) the rate of occurrence is constant, does not change based on time. The probability of an event occurring is proportional to the length of the time period.

b) 2*60 = 120

c) P(x;u) = e^-u u^x/x!

u = 4.

compute probabilities for x = 1, 2 and 3 and sum probabilities

d) u = 6

compute probabilities for x = 0 and 1, sum probabilities then subtract from 1

e) u = 2, compute probability for x = 0