Question

A call centre receives, on average, 10 calls per minute. The highest number of calls received in any minute is 15. For any randomly selected minute, find the probability that they will receive:

i. At least 13 calls

ii. At most 2 calls

iii. 7 to 9 calls

iv. Find the Mean, Variance and Standard Deviation of the distribution

show all working

Answer 1

i)

The provided mean is λ=10.

We need to compute Pr(X≥13). Therefore, the following is obtained:

ii)

We need to compute Pr(X≤2). Therefore, the following is obtained:

iii)

We need to compute Pr(7≤X≤9). Therefore, the following is obtained:

iv)

Mean = λ=10.

variance = λ=10.

Standard deviation = sqrt(10) =3.162