A particular manufacturing company has exactly two manufacturing plants–Plants A and B. A consultant, using data about the company's past...

Owning The Dataset

Table 1: Text Analysis

Table 2: Chart Analysis

Key Insights

1. Only in-house production can result in profits within $1 of average (probability 18.75%).
2. Subcontracting leads to extreme results: equally likely to be much better or much worse than average (no middle outcomes).
3. For large orders, the company overwhelmingly prefers in-house (75% of cases), favoring more consistent and better profits.

Step-by-Step Solution

Question 1: Manufacturing Path Probability

Complete Statement:

The chart indicates that, for an order selected at random from those consisting of more units than could be produced by Plant A, the probability that the company's profit per unit on that order was within $1 of the average is equal to the sum of [BLANK 1] and...

Breaking Down the Statement

• Statement Breakdown 1:
  • Key Phrase: order selected at random from those consisting of more units than could be produced by Plant A
  • Meaning: The focus is only on orders larger than Plant A's capacity.
  • Relation to Chart: All probabilities in the tree apply only to these large orders – it's the root of the decision tree.
  • Important Implications: Probabilities shown later in the tree are conditional on this starting point.

• Statement Breakdown 2:
  • Key Phrase: probability that the company's profit per unit on that order was within $1 of the average
  • Meaning: Looking for orders that achieved a 'within $1 of average' profit outcome.
  • Relation to Chart: Must consider each possible branch that can result in this outcome.
  • Important Implications: We must add up these probabilities.

• What is needed: The probability from the manufacturing branch that results in a profit within $1 of average.

Solution:

• Condensed Solution Implementation:
  Multiply probability of manufacturing (0.75) by probability of 'within $1' given manufacturing (0.25).
• Necessary Data points:
  Probability for manufacturing: 0.75; Probability for 'within $1' given manufacturing: 0.25.
• Calculations Estimations:
  \(0.75 \times 0.25 = 0.1875\)
• Comparison to Answer Choices:
  0.1875 matches an answer choice, so this is the correct value for BLANK 1.

FINAL ANSWER Blank 1: 0.1875

Question 2: Subcontracting Path Probability

Complete Statement:

...and [BLANK 2]

Breaking Down the Statement

• Statement Breakdown 1:
  • Key Phrase: and [BLANK 2]
  • Meaning: This is the other portion of the probability sum, referring to the subcontracting path.
  • Relation to Chart: Represents probability of getting profit within $1 of average in the subcontracting branch.

• What is needed: The probability from the subcontracting branch that results in a profit within $1 of average.

Solution:

• Condensed Solution Implementation:
  Multiply probability of subcontracting (0.25) by probability of 'within $1' given subcontracting (0.50).
• Necessary Data points:
  Probability for subcontracting: 0.25; Probability for 'within $1' given subcontracting: 0.50.
• Calculations Estimations:
  \(0.25 \times 0.50 = 0.125\)
• Comparison to Answer Choices:
  0.125 matches an answer choice for BLANK 2.

FINAL ANSWER Blank 2: 0.125

Summary

To find the required probability, add the probabilities of both manufacturing and subcontracting branches leading to 'profit within $1 of average'. The total is \(0.1875 + 0.125 = 0.3125\).

Question Independence Analysis

BLANK 1 and BLANK 2 correspond to distinct branches (manufacturing and subcontracting, respectively), but both are required to find the total probability as specified by the question. Thus, they are related and dependent in the context of solving the problem.