Probability questions

Question

A company's customer service department monitors the time it takes to resolve customer complaints. The resolution times are distributed with a mean of 35 minutes and a standard deviation of 8 minutes. Find the probability that

a) the customer complaints are resolved within 30 minutes

b) the customer complaints are resolved after 50 minutes

c) the customer complaints are resolved within 40-55 minutes​

Answer 1

It should be stated (or assumed) that the times follow an approximately Normal distribution, otherwise some fancier tricks are required.

Although this can be solved using z-scores (which is what the video above seems to do, and that's a perfectly valid method), this is no longer necessary since technology is widely available. On a TI-84 for example, one can use the normalcdf() function [2nd > VARS > DISTR, then pick the second item in the list]:

normalcdf(lower_x, upper_x, μ, σ)

which gives the proportion/probability/area between lower_x and upper_x in a Normal distribution with mean μ and standard deviation σ. When there's no lower limit (your part (a)), use a very negative number, and when there's no upper limit (your part(b)), use a very large positive number. Specifically you would use:

a) normalcdf(-99999, 30, 35, 8)

b) normalcdf(50, 99999, 35, 8)

c) normalcdf(40, 55, 35, 8)

If you don't have/like the TI, there are plenty of free online calculators that do the same sort of thing (I'm personally a big fan of Geogebra).

Answer 2

Hello!

Please take a look at the video.

Please let me know if you need any further explanations.

Thanks,

Erin