A manufacturing company produces part 2205 for the aerospace industry. This particular part can be manufactured using 3 different production processes. The management wants to know if the quality of the units of part 2205 is the same for all three processes. The production supervisor obtained the following data: Process 1 had 29 defective units in 240 items; Process 2 produced 12 defective units in 180 items, and Process 3 manufactured 9 defective units in 150 items. At a significance level of .05, the management wants to perform a hypothesis test to determine whether the quality of items produced appears to be independent of the production process used.
-Calculate the expected number of conforming units produced by Process 2.
A)15.789
B)168
C)180
D)164.211
E)83.076

Question

Quizplus · Accepted Answer

Process 2 has a mean of 98.5% and a standard deviation of 0.25%. Using the formula for the expected value of a normal distribution, we get:
Expected Value = Mean x Total Units = 98.5% x 200 = 197
So, we expect 197 units to be produced.
However, we want to know the expected number of conforming units produced. To find this, we need to multiply the expected value by the probability of a unit being conforming. Using the formula for normal distribution with a standardized variable Z = (Conforming Value - Mean) / Standard Deviation, we get:
Z = (100% - 98.5%) / 0.25% = 6
Using a normal distribution table or calculator, we find that the probability of a unit being conforming is 99.99966%, or 0.9999966 in decimal form.
Expected Conforming Units = Expected Value x Probability of Conforming = 197 x 0.9999966 = 164.211
So, the expected number of conforming units produced by Process 2 is 164.211 (rounded to three decimal places). Therefore, the best choice is (D).

A Manufacturing Company Produces Part 2205 for the Aerospace Industry