Statistics Question?

Question

The technical support call center for a software company has a mean wait time of 210 seconds, with a standard deviation of 40 s. The management team wants to continue to improve customer satisfaction by setting a wait-time standard. If the company wants 85% of the calls to be answered within a new time specification, what maximum wait time should be used? Thanks in advance.

Answer 1

We want 85% of the calls to be answered within the new time specification, so we must first find the the z-score z₀ such that P(z≤z₀)=0.85. From a table or using a calculator you find z₀=1.036. Now use

z = (x-µ)/σ

to find the corresponding wait time:

1.036 = (x-210)/40,

which gives x=251.45 s.

 

Therefore, 85% of calls should be answered within a maximum wait time of 251.45 s.

Answer 2

As things stand, 68.26% of the wait time values fall withing ± 1 standard deviation of the mean.

 

If the company wants to set a new wait time so that 85% of the calls are answered within 1 standard deviation of the mean, then I think the new average wait time standard, T_mean,  is given by:

 

(68.26%/210 sec.) = (85%)/T_mean

 

T_mean = 261.5 sec.

 

Since, however, the questions asks the new maximum wait time, T_max, we need to calculate thusly:

 

(68.26%/250 sec.) = (85%)/T_mas

 

from which

 

T_max = 311.3 sec.

 

Maralyn, I admit off the top that I'm not necessarily a good statistician.  Don't take my answer as Gospel.