Question

blemish on can (blemish)
crack in can (crack)
improper pull tab location (location)
pull tab missing (missing)
other
a sample of nonconforming cans is selected and each can is categorized according to the reason for nonconformity and which production line produced each can. the contingency table for the reason for nonconformance and production line is shown below.

production line	count	blemish	crack	location	missing	other	total
2	23	52	25	19	6	125
3	32	28	16	14	10	100
total	89	145	58	54	29	375

which of the following is the marginal distribution for production line?
○ line 1 = 150/375, line 2 = 125/375, line 3 = 100/375
○ line 1 = 100/375, line 2 = 125/375, line 3 = 150/375
○ line 1 = 34/150, line 2 = 23/125, line 3 = 32/100
○ line 1 = 13/29, line 2 = 6/29, line 3 = 10/29

Explanation:

Step1: Recall marginal - distribution concept

The marginal distribution of production line is found by dividing the total number of non - conforming cans from each production line by the grand total of non - conforming cans.

Step2: Identify relevant totals

The total number of non - conforming cans from Line 1 is 150, from Line 2 is 125, from Line 3 is 100, and the grand total of non - conforming cans is 375.

Step3: Calculate marginal probabilities

The probability for Line 1 is $\frac{150}{375}$, for Line 2 is $\frac{125}{375}$, and for Line 3 is $\frac{100}{375}$.

Answer:

Line 1 = 150/375, Line 2 = 125/375, Line 3 = 100/375