196 the z value was identified as half of the α value

1.96. The z value was identified as half of the α value of .05, which is .0250. Subtracting
this value from the total area of half of the curve or .5000, gives a value of .4750.
According to the normal Z-table, we find that the corresponding value is 1.96.
Expanding upon the formula can also show the lower confidence limit with the -z value
and upper confidence limit with the +z value. This formula is expressed as, x -z α/2
2

σ/√n<μ< x +z α/2 σ/√n (Black, 2017). Because of the expanded formula, the mean pay
time is between 17.09 days and 19.11 days, expressed mathematically as
17.09<μ<19.11. Based on these calculations, the effectiveness of the new billing system
can now be determined. According to the case, the old billing system showed an
average billing payment time of 39 days. Also, according to the case, the firm made a
claim that prior to implementing the new system, the average payment time was
estimated to be reduced to <19.5 days. The calculations show, that since the new
population mean was less than the upper limit of 19.11 days, the electronic billing
system was successful in reducing the mean payment time by at least 51%.
95% Confidence That µ ≤ 19.5 Days?
Unlike the previous calculation that dealt with the average period a company took
to pay its creditors; this calculation is best suited for the probability of the mean payment
time. If µ ≤ 19.5 days, standard deviation is 4.2 days, Sample (n) is 65; The mean is
calculated at 18.10769231. The computed standard deviation = 3.961230384, this is