Using this partial Z Table, how many units from a month's production run are expected to not satisfy customer requirements for the following process? Upper specification limit: 7.2 Lower specification limit: 4.3 Mean of the process: 5.9 Standard Deviation: 0.65 Monthly production: 450 units

Question

Quizplus · Accepted Answer

First, we need to find the Z-score for the upper specification limit (USL) and lower specification limit (LSL).

Z-score for USL = (USL - Mean)/Standard Deviation = (7.2 - 5.9)/0.65 = 2

Z-score for LSL = (LSL - Mean)/Standard Deviation = (4.3 - 5.9)/0.65 = -2.46

Using the Z table, we can find the probability of a unit falling outside the specification limits. From the Z table, we see that the probability of a unit falling outside the specification limit at a Z-score of 2 is 0.0228. Similarly, the probability of a unit falling outside the specification limit at a Z-score of -2.46 is also 0.0228.

Now, we can find the expected number of units that will not satisfy customer requirements using the following formula:

Expected number of units outside specification limits = Total production * Probability of a unit falling outside specification limits

Expected number of units outside specification limits = 450 * (0.0228+0.0228)

Expected number of units outside specification limits = 20.52

Rounding off to the nearest integer, we get:

Expected number of units outside specification limits = 21

Therefore, the best choice is C) 10, as it is the closest value to the expected number of units that will not satisfy customer requirements.

Using This Partial Z Table, How Many Units from a Month's