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Statistics 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.

Andre W. | Friendly tutor for ALL math and physics coursesFriendly tutor for ALL math and physics ...
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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.

It just occurred to me that the question could also be read as 85% of calls are to be answered below a new time specification. In that case, we have P(z≤z0)=0.85, giving z0=1.036 and x=251.45 s.
William S. | Experienced scientist, mathematician and instructor - WilliamExperienced scientist, mathematician and...
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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, Tmean,  is given by:

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

Tmean = 261.5 sec.

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

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

from which

Tmax = 311.3 sec.

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