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# Two production lines are used to pack sugar into 5 kg ISBN: 9780073401331 38

## Solution for problem 4SE Chapter 2

Statistics for Engineers and Scientists | 4th Edition

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Problem 4SE

Two production lines are used to pack sugar into 5 kg bags. Line 1 produces twice as many bags as does line 2. One percent of the bags from line 1 are defective in that they fail to meet a purity specification, while 3% of the bags from line 2 are defective. A bag is randomly chosen for inspection.

a. What is the probability that it came from line 1?

b. What is the probability that it is defective?

c. If the bag is defective, what is the probability that it came from line 1?

d. If the bag is not defective, what is the probability that it came from line 1?

Step-by-Step Solution:

Step 1 of 5:

Given that there are two lines,line1 and line2 used to pack sugar into bags of 5kg.

Line1 produces bags equal to twice the number of bags produced by line2.

1% of bags from line1 are fail to meet the purity specification and hence are considered as defectives.

3% of bags from line2 are fail to meet the purity specification and hence are considered as defectives.

A bag from the lot is randomly chosen for inspection.

Using all these data we have to find out the required probabilities.

Step 2 of 5:

(a)

Here we have to find the probability that the randomly chosen bag is  from line1.

Let x denotes the number of bags produced by line2.

Then,the total number of bags produced by line1 is equal to 2x,and total number of bags produced by line1 and line2 is equal to x+2x.

Thus,

P(Chosen bag came from line1)= = = =0.6667

Hence,the probability that randomly chosen bag came from line 1 is 0.667.

Step 3 of 5:

(b)

Here we have to find the probability that the randomly chosen bag is defective.

It is given by,

P(Chosen bag is defective)=P(chosen bag is from line 1)*P(defective bags in line1)+P(chosen         bag is from line 2)*P(defective bags in line 2)

= * + * = *0.01+ *0.03

= *0.01+ *0.03

=0.6667*0.01+0.3333*0.03

=0.006667+0.009999

=0.016666

Thus,the probability that the randomly chosen bag is defective is 0.01666.

Step 4 of 5

Step 5 of 5

##### ISBN: 9780073401331

The answer to “Two production lines are used to pack sugar into 5 kg bags. Line 1 produces twice as many bags as does line 2. One percent of the bags from line 1 are defective in that they fail to meet a purity specification, while 3% of the bags from line 2 are defective. A bag is randomly chosen for inspection.a. What is the probability that it came from line 1?________________b. What is the probability that it is defective?________________c. If the bag is defective, what is the probability that it came from line 1?________________d. If the bag is not defective, what is the probability that it came from line 1?” is broken down into a number of easy to follow steps, and 108 words. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. This full solution covers the following key subjects: line, defective, Bags, Probability, came. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. Since the solution to 4SE from 2 chapter was answered, more than 1347 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 4SE from chapter: 2 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM.

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