Question 1193886: Read the following hypothetical case and answer the questions below.
The Indiana Inc. a lead denim manufacturer in New Orleans has productions
sites in four different counties with production ratio at 8:5:3:4. Their key products
are skinny jeans (50%), straight leg jeans (35%) and jeggings (15%). Each of
these products come in two styles - stone washed (60%) and plain (40%). Their
monthly production cost is about $0.95 mn. All products in both styles are
produced at all the four sites, while the manufacture proportion is maintained
across the production sites.
1. The analysts at Indiana Inc intend to draw a sample for a quick analysis.
Propose a probability sampling technique elucidating the steps clearly.
2. The following table shows the sale price for each product:
Sales Prices Skinny Jeans Straight Leg
Jeans Jeggings
Stone Washed $210 $185 $170
Plain $185 $90 $110
3) Given that 5,000 units were produced last month what is the revenue
generated for each product line? Comment about the status of business at
Indiana Inc.
4)If it is known that the product is stone washed jeans what are the chances
that it is skinny jeans?
Answer by parmen(42)   (Show Source):
You can put this solution on YOUR website! **1. Probability Sampling Technique**
**Stratified Sampling**
* **Steps:**
1. **Divide the population into strata:** In this case, the production sites in the four counties can be considered strata.
2. **Determine the sample size for each stratum:** Allocate the sample size to each stratum proportionally to its size within the population. Since the production ratio is 8:5:3:4, allocate samples to each county in this proportion.
3. **Randomly select units within each stratum:** Use a random number generator or a table of random numbers to select the required number of units (e.g., jeans) from each county's production.
**Advantages of Stratified Sampling:**
* Ensures representation from each production site.
* Improves the accuracy of the sample by reducing sampling error.
* Allows for analysis of differences between production sites.
**2. Revenue Generated for Each Product Line**
* **Calculate the number of units produced for each product:**
* Skinny Jeans: 5000 units * 50% = 2500 units
* Straight Leg Jeans: 5000 units * 35% = 1750 units
* Jeggings: 5000 units * 15% = 750 units
* **Calculate revenue for each product and style:**
* **Skinny Jeans:**
* Stone Washed: 2500 units * 60% * $210 = $315,000
* Plain: 2500 units * 40% * $185 = $185,000
* **Straight Leg Jeans:**
* Stone Washed: 1750 units * 60% * $185 = $194,250
* Plain: 1750 units * 40% * $90 = $63,000
* **Jeggings:**
* Stone Washed: 750 units * 60% * $170 = $76,500
* Plain: 750 units * 40% * $110 = $33,000
* **Total Revenue:** $315,000 + $185,000 + $194,250 + $63,000 + $76,500 + $33,000 = $866,750
**Comment on Business Status:**
* Based on the revenue figures, Indiana Inc. appears to be generating significant revenue.
* Skinny jeans and stone-washed jeans are the highest-revenue generators.
* Further analysis would be needed to assess profitability, market share, and competitive landscape to fully evaluate the business status.
**3. Probability of Skinny Jeans given Stone Washed**
* **Let:**
* A: Event that the product is Skinny Jeans
* B: Event that the product is Stone Washed
* **Given:**
* P(A) = Probability of Skinny Jeans = 50% = 0.5
* P(B) = Probability of Stone Washed = 60% = 0.6
* P(A and B) = Probability of Skinny Jeans and Stone Washed = 0.5 * 0.6 = 0.3
* **Use Bayes' Theorem:**
* P(A | B) = P(B | A) * P(A) / P(B)
* P(A | B) = (P(A and B) / P(A)) * P(A) / P(B)
* P(A | B) = P(A and B) / P(B)
* P(A | B) = 0.3 / 0.6 = 0.5
* **Therefore, the probability that the product is Skinny Jeans given that it is Stone Washed is 0.5 or 50%.**
I hope this comprehensive analysis is helpful!
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