Question

The switchboard in a Minneapolis law office gets an average of 5.5 incoming phone calls during the noon hour on Mondays. Experience shows that the existing staff can handle up to six calls in an hour. Let X = the number of calls received at noon. What is the standard deviation of X?

Answer 1

Standard deviation of X = 2.3452 calls

Explanation:

This is a Poisson distribution problem with an average (μ) of 5.5 number of incoming calls during the noon hour on Mondays.

Therefore, the standard deviation for the number of calls received, X, is represented by:

a. σ = √µ

Thus;

X ~ P(5.5); µ = 5.5; σ = √5.5 ≈ 2.3452 calls

Answer 2

2.35 calls

Explanation:

The presented scenario can be modeled by a Poisson distribution with an average number of calls (μ) of 5.5 during the noon hour on Mondays.

Therefore, the standard deviation for the number of calls received, X, is given by:

`\sigma =\sqrt \mu\\\sigma =\sqrt5.5\\\sigma =2.35\ calls`

The standard deviation of X is 2.35 calls.