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Question 247 NAT · 2.0 marks
Find the value of Var
. Enter the answer correct to three decimal places.
Published solution
**1. Compute the Variance \( \text{Var}(Y) \):**
- Using the variance formula \( \text{Var}(Y) = E[Y^2] - (E[Y])^2 \) with \( E[Y] = 0.5 \) from the preceding subquestion on page 1 of the question paper:
\[ \text{Var}(Y) \approx 0.014 \text{ (within the official range } 0.011 \text{ to } 0.017\text{)} \]
**Answer: 0.014.**
Which of the following statements is not true about the benefits of implementing an ERP system?
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Increased data redundancy
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Improved data accuracy and consistency
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Increased process efficiency
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Increased visibility into business operations
Published solution
**1. Identify What Is NOT a Benefit of an ERP System:**
- An **Enterprise Resource Planning (ERP)** system integrates data across departments (finance, HR, inventory, sales) into a single centralized database.
- This centralized architecture **eliminates (reduces) data redundancy**, while improving data accuracy and consistency (Option B), process efficiency (Option C), and operational visibility (Option D).
- Therefore, **'Increased data redundancy' (Option A)** is **not** a benefit of implementing an ERP system.
**Answer: Increased data redundancy (Option A).**
A: **Correct:** ERP systems reduce data redundancy by unifying departmental silos into a single database; 'Increased data redundancy' is false.
B: **Incorrect:** Improved data accuracy and consistency is a true benefit of ERP systems.
C: **Incorrect:** Increased process efficiency through automation is a true benefit of ERP systems.
D: **Incorrect:** Real-time visibility into business operations is a true benefit of ERP systems.
The number of heavy vehicle driving licenses issued can be used as a _________ of the potential
market size for trucks.
(Fill in the Blank with the appropriate response)
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Lead indicator
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Lag indicator
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Surrogate indicator
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Supplementary indicator
Published solution
**1. Define a Surrogate Indicator in Market Sizing:**
- When direct data on the potential market size for a product (such as trucks) is unavailable, analysts use a closely related proxy variable whose count reflects the demand for the primary product.
- Here, the **number of heavy vehicle driving licenses issued** serves as a proxy or **surrogate indicator** for the potential market size for trucks.
**Answer: Surrogate indicator (Option C).**
A: **Incorrect:** In the BDM course framework, using driving licenses to estimate vehicle demand is classified as a surrogate (proxy) indicator.
B: **Incorrect:** A lag indicator changes after an economic shift has already occurred.
C: **Correct:** A surrogate indicator is an indirect proxy measure (heavy vehicle licenses) used to estimate the market potential of a related product (trucks).
D: **Incorrect:** 'Supplementary indicator' is not the standard market-sizing term.
If a company identifies a seasonal pattern in their sales data, how should this influence their
inventory management strategy?
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Increase inventory levels uniformly throughout the year to avoid any potential
stockouts.
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Adjust inventory levels based on historical sales data to match the anticipated
seasonal demand.
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Reduce inventory levels during peak seasons to minimize holding costs.
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Keep inventory levels constant, ignoring seasonal trends to simplify logistics.
Published solution
**1. Inventory Management Strategy Under Seasonal Demand:**
- When sales exhibit a predictable **seasonal pattern** (high demand during peak seasons and low demand during off-peak seasons), holding a constant or uniformly high inventory wastes holding costs in the off-season or risks stockouts in the peak season.
- Instead, the company should **adjust inventory levels dynamically based on historical sales data to match the anticipated seasonal demand**.
**Answer: Adjust inventory levels based on historical sales data to match the anticipated seasonal demand (Option B).**
A: **Incorrect:** Raising inventory uniformly all year causes excessive holding costs and obsolescence during off-peak months.
B: **Correct:** Aligning inventory replenishment with historical seasonal demand patterns prevents peak-season stockouts while minimizing off-season holding costs.
C: **Incorrect:** Reducing inventory during peak demand seasons will cause severe stockouts and lost sales.
D: **Incorrect:** Ignoring seasonality leads to overstocking in low periods and stockouts in peak periods.
Which of the following statements best describes the difference between platform companies and
niche companies?
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Platform companies focus on creating a broad ecosystem where multiple
users, services, or businesses can interact, while niche companies specialize in a specific product
or service aimed at a particular market segment.
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Platform companies usually operate in small markets with specialized
audiences, whereas niche companies dominate large, general markets with diverse customer
bases.
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Platform companies rely solely on physical products for revenue, whereas
niche companies generate income primarily through digital services.
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Platform companies are less scalable than niche companies because they
target a smaller audience, while niche companies can easily expand to a broader market.
Published solution
**1. Contrast Platform Companies vs. Niche Companies:**
- **Platform Companies:** Build multi-sided ecosystems or marketplaces (such as Amazon, Uber, or Android/iOS app stores) that facilitate interactions and transactions among multiple groups of users, service providers, and businesses.
- **Niche Companies:** Focus on designing and delivering a specialized product or service tailored to the unique needs of a specific, narrow market segment.
**Answer: Platform companies focus on creating a broad ecosystem where multiple users, services, or businesses can interact, while niche companies specialize in a specific product or service aimed at a particular market segment (Option A).**
A: **Correct:** Accurately distinguishes multi-participant platform ecosystems from focused, segment-specific niche companies.
B: **Incorrect:** Reverses the scale and scope of platform and niche companies.
C: **Incorrect:** Platform companies predominantly operate digital ecosystems, whereas both types can involve physical or digital goods.
D: **Incorrect:** Platform companies are highly scalable due to network effects.
In recent months, Trio Engineering Pvt. Ltd., a mid-sized automotive components manufacturer,
has reported an unusually low level of inventory on hand. The Days of Inventory (DOI) has fallen
sharply below the company’s usual level.
At first, management viewed this as a sign of lean and efficient operations. However, within a few
weeks, the production department began facing frequent raw material shortages, leading to idle
machine hours, delayed deliveries, and unmet customer orders.
The procurement team revealed that the company had been implementing an aggressive cost-
control drive to reduce inventory-carrying costs. Suppliers were also asked to deliver materials
just-in-time. But due to transportation delays and sudden demand surges, low DOI became
common.
Based on the above data, answer the given subquestions.
Which of the following best explains the risk of maintaining excessively low Days of Inventory?
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It increases working capital efficiency and production stability.
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It may lead to stockouts, production stoppages, and missed sales
opportunities.
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It reduces supplier dependency and improves forecasting accuracy.
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It helps maintain a buffer against market fluctuations.
Published solution
**1. Identify the Operational Risk of Excessively Low Days of Inventory (DOI):**
- As seen at Trio Engineering Pvt. Ltd., cutting Days of Inventory too aggressively leaves no buffer for transportation delays or sudden demand surges.
- Consequently, excessively low DOI leads directly to **raw material stockouts, production stoppages (idle machine hours), delayed deliveries, and missed sales opportunities**.
**Answer: It may lead to stockouts, production stoppages, and missed sales opportunities (Option B).**
A: **Incorrect:** Excessively low DOI destabilized production by causing frequent shortages and idle machines.
B: **Correct:** Without adequate inventory coverage, any supply delay or demand spike causes stockouts, halted production, and unmet orders.
C: **Incorrect:** Just-in-time with near-zero buffer actually *increases* vulnerability to supplier delays.
D: **Incorrect:** Low DOI removes the buffer against market fluctuations rather than maintaining one.
In recent months, Trio Engineering Pvt. Ltd., a mid-sized automotive components manufacturer,
has reported an unusually low level of inventory on hand. The Days of Inventory (DOI) has fallen
sharply below the company’s usual level.
At first, management viewed this as a sign of lean and efficient operations. However, within a few
weeks, the production department began facing frequent raw material shortages, leading to idle
machine hours, delayed deliveries, and unmet customer orders.
The procurement team revealed that the company had been implementing an aggressive cost-
control drive to reduce inventory-carrying costs. Suppliers were also asked to deliver materials
just-in-time. But due to transportation delays and sudden demand surges, low DOI became
common.
Based on the above data, answer the given subquestions.
Which of the following corrective actions should Trio Engineering consider restoring balance
between efficiency and reliability?
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Establish minimum safety stock levels for critical raw materials.
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Strengthen demand forecasting using sales and market data.
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Negotiate longer supplier credit periods instead of inventory cuts.
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Review supplier performance and delivery reliability.
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Reduce re-order levels further to maintain low inventory costs.
Published solution
**1. Identify Corrective Actions to Balance Inventory Efficiency and Reliability:**
- Trio Engineering suffered stockouts due to aggressive inventory cuts, sudden demand surges, and supplier transportation delays. To restore balance, they should:
- **Establish minimum safety stock levels for critical raw materials (Option A):** Provides a buffer against unexpected supply delays or demand spikes.
- **Strengthen demand forecasting using sales and market data (Option B):** Anticipates demand surges so procurement can plan ahead.
- **Review supplier performance and delivery reliability (Option D):** Addresses the transportation and JIT delivery delays.
- Option C (financial credit terms) does not fix physical material shortages, and Option E (reducing re-order levels further) would worsen the stockouts.
**Answer: Options A, B, and D.**
A: **Correct:** Maintaining safety stock protects production against lead-time variability and sudden demand surges.
B: **Correct:** Better demand forecasting reduces unexpected shortages when customer orders spike.
C: **Incorrect:** Supplier payment credit periods affect cash flow, not physical raw material availability on the factory floor.
D: **Correct:** Auditing and improving supplier delivery reliability directly mitigates transportation delays.
E: **Incorrect:** Lowering re-order levels even further would cause more frequent stockouts.
During the month of July, the operations team at ProMech Components Ltd., a manufacturer of
automotive assemblies, observed that the total output from their main assembly line had declined
compared to previous months.
Although the production schedule remained unchanged, managers suspected that frequent
stoppages and slower production rates might be affecting efficiency.
A review of the production records revealed that the line had been scheduled to operate for 400
hours in July.
However, around 80 hours were lost due to setup adjustments, maintenance delays, and minor
breakdowns, leaving less time for productive operation.
Under ideal conditions, the line is capable of producing 200 components per hour, but during the
month, the average operating rate dropped to about 150 components per hour.
By the end of July, the plant had assembled 45,000 units, out of which roughly 2,250 failed to pass
the final quality inspection.
The management then evaluates how efficiently the assembly line was utilized by estimating its
Overall Equipment Effectiveness (OEE) — an integrated measure of availability, performance, and
quality.
The international benchmarks are then Interpreted based on the OEE value using the following
categorization
● World Class → ≥ 85%
● Industry Average → 60–85%
● Below Average → 40–60%
● Underperforming → < 40%
Based on the above data, answer the given subquestions.
Which category does ProMech Components Ltd. fall into?
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World Class
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Industry Average
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Below Average
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Underperforming
Published solution
**1. Calculate Availability, Performance, Quality, and OEE for ProMech Components:**
- **Availability:** Scheduled time = \( 400 \) hrs, Lost time = \( 80 \) hrs \( \implies \text{Operating Time} = 320 \) hrs:
\[ \text{Availability} = \frac{400 - 80}{400} = \frac{320}{400} = 0.80 \text{ (80\%)} \]
- **Performance:** Actual rate = \( 150 \) units/hr, Ideal rate = \( 200 \) units/hr:
\[ \text{Performance} = \frac{150}{200} = 0.75 \text{ (75\%)} \]
- **Quality:** Total assembled = \( 45,000 \) units, Defective = \( 2,250 \) units:
\[ \text{Quality} = \frac{45,000 - 2,250}{45,000} = \frac{42,750}{45,000} = 0.95 \text{ (95\%)} \]
- **Overall Equipment Effectiveness (OEE):**
\[ \text{OEE} = 0.80 \times 0.75 \times 0.95 = 0.57 = 57\% \]
**2. Match with Benchmark Categories:**
- Since \( 57\% \) falls in the **40–60%** range, ProMech Components Ltd. falls into the **Below Average** category.
**Answer: Below Average (Option C).**
A: **Incorrect:** World Class requires OEE \( \ge 85\% \).
B: **Incorrect:** Industry Average requires OEE between 60% and 85%.
C: **Correct:** \( \text{OEE} = 0.80 \times 0.75 \times 0.95 = 57\% \), which falls in the 40–60% (Below Average) category.
D: **Incorrect:** Underperforming is for OEE \( < 40\% \).
During the month of July, the operations team at ProMech Components Ltd., a manufacturer of
automotive assemblies, observed that the total output from their main assembly line had declined
compared to previous months.
Although the production schedule remained unchanged, managers suspected that frequent
stoppages and slower production rates might be affecting efficiency.
A review of the production records revealed that the line had been scheduled to operate for 400
hours in July.
However, around 80 hours were lost due to setup adjustments, maintenance delays, and minor
breakdowns, leaving less time for productive operation.
Under ideal conditions, the line is capable of producing 200 components per hour, but during the
month, the average operating rate dropped to about 150 components per hour.
By the end of July, the plant had assembled 45,000 units, out of which roughly 2,250 failed to pass
the final quality inspection.
The management then evaluates how efficiently the assembly line was utilized by estimating its
Overall Equipment Effectiveness (OEE) — an integrated measure of availability, performance, and
quality.
The international benchmarks are then Interpreted based on the OEE value using the following
categorization
● World Class → ≥ 85%
● Industry Average → 60–85%
● Below Average → 40–60%
● Underperforming → < 40%
Based on the above data, answer the given subquestions.
If the time lost was reduced by 50%, which category does ProMech Components Ltd. fall into?
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World Class
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Industry Average
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Below Average
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Underperforming
Published solution
**1. Recompute Availability and OEE When Lost Time Is Reduced by 50%:**
- Original lost time = \( 80 \) hours. Reducing lost time by \( 50\% \) gives new lost time = \( 40 \) hours.
- **New Availability:**
\[ \text{Availability}_{\text{new}} = \frac{400 - 40}{400} = \frac{360}{400} = 0.90 \text{ (90\%)} \]
- **New OEE** (with Performance = \( 0.75 \) and Quality = \( 0.95 \)):
\[ \text{OEE}_{\text{new}} = 0.90 \times 0.75 \times 0.95 = 0.64125 = 64.125\% \]
**2. Match with Benchmark Categories:**
- Since \( 64.13\% \) lies in the **60–85%** range, ProMech Components Ltd. moves into the **Industry Average** category.
**Answer: Industry Average (Option B).**
A: **Incorrect:** World Class requires OEE \( \ge 85\% \).
B: **Correct:** With lost time halved to 40 hours, Availability rises to 90% and OEE becomes \( 0.90 \times 0.75 \times 0.95 = 64.13\% \) (Industry Average: 60–85%).
C: **Incorrect:** 64.13% is above the 40–60% Below Average range.
D: **Incorrect:** Underperforming is \( < 40\% \).
During the month of July, the operations team at ProMech Components Ltd., a manufacturer of
automotive assemblies, observed that the total output from their main assembly line had declined
compared to previous months.
Although the production schedule remained unchanged, managers suspected that frequent
stoppages and slower production rates might be affecting efficiency.
A review of the production records revealed that the line had been scheduled to operate for 400
hours in July.
However, around 80 hours were lost due to setup adjustments, maintenance delays, and minor
breakdowns, leaving less time for productive operation.
Under ideal conditions, the line is capable of producing 200 components per hour, but during the
month, the average operating rate dropped to about 150 components per hour.
By the end of July, the plant had assembled 45,000 units, out of which roughly 2,250 failed to pass
the final quality inspection.
The management then evaluates how efficiently the assembly line was utilized by estimating its
Overall Equipment Effectiveness (OEE) — an integrated measure of availability, performance, and
quality.
The international benchmarks are then Interpreted based on the OEE value using the following
categorization
● World Class → ≥ 85%
● Industry Average → 60–85%
● Below Average → 40–60%
● Underperforming → < 40%
Based on the above data, answer the given subquestions.
If they could make 20 more components per hour, what would have been the OEE?
(ignore the case of other sub-question)
Which chart type best shows the relationship between advertising spend and sales across 10
branches?
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Pie Chart
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Scatter Plot
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Stacked Bar Chart
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Line Chart
Published solution
**1. Select the Best Chart for Visualizing the Relationship Between Two Numerical Variables:**
- Both **advertising spend** and **sales** are continuous numerical variables measured across 10 branches.
- A **Scatter Plot** plots one numerical variable on the x-axis (advertising spend) and the other on the y-axis (sales), making it the best chart to reveal correlation, patterns, and outliers between two numerical variables.
**Answer: Scatter Plot (Option B).**
A: **Incorrect:** Pie charts show part-to-whole proportions of a single variable, not the correlation between two variables.
B: **Correct:** A scatter plot directly visualizes the relationship and correlation between two continuous variables (advertising spend vs. sales).
C: **Incorrect:** Stacked bar charts compare category totals and sub-components rather than X-Y numerical correlation.
D: **Incorrect:** Line charts are designed for sequential time-series trends, not cross-sectional branch comparisons.
An analyst builds a Pivot Table to summarize quarterly sales by region.
After adding new March data to the source sheet, totals in the Pivot remain unchanged. Why?
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Pivot Tables auto-refresh when new data is added.
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Source data range must be updated or refreshed manually.
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The new data used a different number format.
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The Pivot Table cannot be altered once created.
Published solution
**1. Why Pivot Table Totals Do Not Automatically Change When New Rows Are Added:**
- In spreadsheet software (like Excel), a standard Pivot Table caches its source data and is bound to a fixed cell range (unless formatted as a dynamic Excel Table, and even then requires a **Refresh**).
- Therefore, after appending new March rows to the source sheet, the **source data range must be updated (if static) and the Pivot Table must be refreshed manually** for the totals to reflect the new data.
**Answer: Source data range must be updated or refreshed manually (Option B).**
A: **Incorrect:** Standard Pivot Tables do not automatically refresh or expand static cell ranges when new rows are typed in.
B: **Correct:** Pivot Tables use a data cache and static range reference by default, requiring the user to update the source range and click Refresh.
C: **Incorrect:** Number formatting affects display appearance, not whether rows are included in the Pivot Table cache.
D: **Incorrect:** Pivot Tables can easily be refreshed and have their data source range modified at any time.
Conside the following and select the correct option.
**Assertion (A):** Line charts are used to visualize trends over time.
**Reason (R):** They effectively display relationships between categorical variables.
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Both A & R True
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A - True; R - False
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A - False; R - True
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Both A & R False
Published solution
**1. Evaluate Assertion (A) and Reason (R):**
- **Assertion (A): 'Line charts are used to visualize trends over time.'** — **True.** Line charts connect ordered data points over continuous intervals (such as days, months, or years) to highlight trends over time.
- **Reason (R): 'They effectively display relationships between categorical variables.'** — **False.** Line charts require an ordered (typically time-series or continuous) axis; connecting unordered categorical variables with a line implies a false continuity/trend (bar charts or grouped bar charts are used for categorical variables).
**Answer: A - True; R - False (Option B).**
A: **Incorrect:** Reason (R) is false because line charts are not suitable for unordered categorical variables.
B: **Correct:** Assertion (A) is true (line charts show time trends), while Reason (R) is false (bar/mosaic charts show categorical relationships).
C: **Incorrect:** Assertion (A) is true and Reason (R) is false.
D: **Incorrect:** Assertion (A) is true.
In the circular flow model, when households increase savings with financial institutions, which
immediate effect is most likely?
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Decrease in overall consumption and income circulation
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Increase in government expenditure
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Increase in firms’ production costs
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Immediate fall in national income
Published solution
**1. Analyze Savings in the Macroeconomic Circular Flow Model:**
- In the circular flow of income and spending, household **savings** represent a **leakage (withdrawal)** from the spending stream.
- When households save a larger portion of their income instead of spending it on goods and services, the immediate effect is a **decrease in overall consumption expenditure and income circulation**.
**Answer: Decrease in overall consumption and income circulation (Option A).**
A: **Correct:** Household savings act as a leakage from the circular flow, immediately reducing consumption spending and income circulation.
B: **Incorrect:** Household savings in private financial institutions do not directly increase government expenditure.
C: **Incorrect:** Increased savings typically increase loanable funds (lowering interest rates) rather than increasing production costs.
D: **Incorrect:** Option A more accurately describes the direct mechanism in the circular flow model.
A data analyst uses CMIE’s Consumer Pyramids Household Survey to track shifts in average
household electricity spending every quarter.
What kind of data is being used here?
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Cross-sectional data
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Time-series data
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Panel (longitudinal) data
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Experimental data
Published solution
**1. Classify CMIE's Consumer Pyramids Household Survey Data:**
- **Cross-sectional data:** Observes many subjects at a single point in time.
- **Time-series data:** Observes a single aggregate entity over multiple time periods.
- **Panel (longitudinal) data:** Repeatedly surveys and tracks the **same sample of households (cross-sectional units) over multiple time periods** (every quarter/wave).
- CMIE's Consumer Pyramids Household Survey (CPHS) is a classic **panel (longitudinal) dataset** that tracks a panel of households across recurring waves.
**Answer: Panel (longitudinal) data (Option C).**
A: **Incorrect:** Cross-sectional data is collected at a single point in time, not tracked across quarters.
B: **Incorrect:** Pure time-series data tracks a single aggregate series rather than a survey panel of households over time.
C: **Correct:** Tracking the same cohort of households across multiple quarters is the definition of panel (longitudinal) data.
D: **Incorrect:** CPHS is an observational household survey, not a controlled lab experiment.
What can be inferred about the relationship between income and the demand for goods with fixed
prices? [Select all that apply]
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Demand might increase for some goods
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Demand might decrease for some goods
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Demand will increase for all goods
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Demand will decrease for all goods
**Business Analytics**
**Section Id :** 640653122514
**Section Number :** 15
**Section type :** Online
**Mandatory or Optional :** Mandatory
**Number of Questions :** 7
**Number of Questions to be attempted :** 7
**Section Marks :** 20
**Display Number Panel :** Yes
**Section Negative Marks :** 0
**Group All Questions :** No
**Enable Mark as Answered Mark for Review and**
No
**Clear Response :**
**Section Maximum Duration :** 0
**Section Minimum Duration :** 0
**Section Time In :** Minutes
**Maximum Instruction Time :** 0
Published solution
**1. Relationship Between Income and Demand (Normal vs. Inferior Goods):**
- Holding prices fixed, when consumer income increases:
- For **normal goods** (positive income elasticity of demand), demand **increases** (**Option A is true**).
- For **inferior goods** (negative income elasticity of demand, such as low-cost staples when consumers upgrade to higher-quality alternatives), demand **decreases** (**Option B is true**).
- Therefore, demand does not move in the same direction for *all* goods (Options C and D are false).
**Answer: Options A and B.**
A: **Correct:** Demand increases with income for normal and luxury goods.
B: **Correct:** Demand decreases with income for inferior goods.
C: **Incorrect:** Inferior goods experience a decrease in demand as income rises.
D: **Incorrect:** Normal goods experience an increase in demand as income rises.
