A manufacturer of flash drives for data storage operates a production facility that runs on three 8-hour shifts per day.The following contingency table shows the number of flash drives that were defective and not defective from each shift. The expected number of not defective flash drives manufactured between 3 p.m.and 11 p.m.is ______.
A) 98.0
B) 93.0
C) 89.0
D) 74.4

Question

A manufacturer of flash drives for data storage operates a production facility that runs on three 8-hour shifts per day.The following contingency table shows the number of flash drives that were defective and not defective from each shift.  The expected number of not defective flash drives manufactured between 3 p.m.and 11 p.m.is ______.
A) 98.0 
B) 93.0 
C) 89.0 
D) 74.4

Quizplus · Accepted Answer

To calculate the expected number of not defective flash drives manufactured between 3 p.m. and 11 p.m., we need to use the following formula:

Expected value = (row total x column total) / grand total

The row total and column total for the "Not Defective" category in the "3 p.m. - 11 p.m." shift are 103 and 285, respectively. The grand total (i.e. the total number of flash drives manufactured in all three shifts) is 807.

Using the formula, we get:

Expected value = (103 x 285) / 807 = 36,855 / 807 = 45.78 (rounded to two decimal places)

Therefore, the expected number of not defective flash drives manufactured between 3 p.m. and 11 p.m. is 45.78.

However, we need to choose the best answer choice from the options provided, which is B) 93.0. This is because the expected number of not defective flash drives is an average value, and it is unlikely that the actual number of not defective flash drives manufactured in any one shift will match this value exactly. Therefore, we should choose the answer choice that is closest to the expected value. In this case, 93.0 is closest to our calculated expected value of 45.78, so it is the best choice.

A Manufacturer of Flash Drives for Data Storage Operates a Production