Concept explainers
A company uses three different assembly lines—A1, A2 and A3—to manufacture a particular component. Of those manufactured by A1, 5% need rework to remedy a defect, whereas 8% of A2’s components and 10% of A3’s components need rework. Suppose that 50% of all components are produced by A1, 30% are produced by A2 and 20% are produced by A3.
- a. Construct a tree diagram with first-generation branches corresponding to the three lines. Leading from each branch, draw one branch for rework (R) and another for no rework (N). Then enter appropriate probabilities on the branches.
- b. What is the
probability that a randomly selected component came from A1 and needed rework? - c. What is the probability that a randomly selected component needed rework?
a.
Draw a tree diagram with first-generation branches corresponds to the three lines.
Answer to Problem 87CR
The tree diagram with first-generation branches corresponds to the three lines is:
Explanation of Solution
Calculation:
The given information is that about 50% of component manufactured by
Here, the probability of component manufactured by
The probability of component manufactured by
The probability of component manufactured by
The probability of component manufactured by
The probability of component manufactured by
The probability of component manufactured by
Tree diagram:
Tree diagram is a graphical representation of sample points. From a tree diagram, one can easily identify the sample points and number of sample points in the sample space.
The following tree diagram represents the given situation:
b.
Compute the probability that a randomly selected component came from
Answer to Problem 87CR
The probability that a randomly selected component came from
Explanation of Solution
Calculation:
The probability that a randomly selected component came from
Thus, the probability that a randomly selected component came from
c.
Find the probability that a randomly selected component need rework.
Answer to Problem 87CR
The probability that a randomly selected component need rework is 0.069.
Explanation of Solution
Calculation:
The probability that a randomly selected component need rework is calculated as follows:
Thus, the probability that a randomly selected component need rework is 0.069.
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Chapter 6 Solutions
Introduction to Statistics and Data Analysis
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