A company introduce a new product in the market and expects to make a profit of Rs. 2.5 lakh during the first year if the demand is ‘good’; Rs. 1.5 lakh if the demand is ‘moderate’; and a loss of Rs. 1 lakh if the demand is ‘poor’. Market research studies indicate that the probabilities for the demand to be good and moderate are 0.2 and 0.5, respectively. Find the company’s expected profit and standard deviation.

Question

12-02-2024
Business

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A company introduce a new product in the market and expects to make a profit of Rs. 2.5 lakh during the first year if the demand is ‘good’; Rs. 1.5 lakh if the demand is ‘moderate’; and a loss of Rs. 1 lakh if the demand is ‘poor’. Market research studies indicate that the probabilities for the demand to be good and moderate are 0.2 and 0.5, respectively. Find the company’s expected profit and standard deviation.

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Answer:

the company's standard deviation in profit is approximately Rs. 46,903.94.

Explanation:

To find the company's expected profit and standard deviation, we can use the concept of expected value and variance.

1. **Expected Profit:**

The expected profit is calculated by multiplying each possible profit outcome by its respective probability and summing them up.

Expected Profit = (Probability of Good Demand * Profit in Good Demand) + (Probability of Moderate Demand * Profit in Moderate Demand) + (Probability of Poor Demand * Profit in Poor Demand)

Let's plug in the given values:

Expected Profit = (0.2 * Rs. 2.5 lakh) + (0.5 * Rs. 1.5 lakh) + (0.3 * (-Rs. 1 lakh))

Expected Profit = (0.2 * 250000) + (0.5 * 150000) + (0.3 * -100000)

Expected Profit = (50000) + (75000) + (-30000)

Expected Profit = Rs. 95000

So, the company's expected profit is Rs. 95,000.

2. **Standard Deviation:**

The standard deviation measures the dispersion or spread of the possible profits around the expected profit.

To find the standard deviation, we need to calculate the variance first.

Variance = (Probability of Good Demand * (Profit in Good Demand - Expected Profit)^2) + (Probability of Moderate Demand * (Profit in Moderate Demand - Expected Profit)^2) + (Probability of Poor Demand * (Profit in Poor Demand - Expected Profit)^2)

Let's calculate:

Variance = (0.2 * (250000 - 95000)^2) + (0.5 * (150000 - 95000)^2) + (0.3 * (-100000 - 95000)^2)

Variance = (0.2 * 155000^2) + (0.5 * 55000^2) + (0.3 * 195000^2)

Variance = (0.2 * 24025000000) + (0.5 * 3025000000) + (0.3 * 38025000000)

Variance = 4805000000 + 1512500000 - 11407500000

Variance = 2201000000

Now, the standard deviation is the square root of the variance.

Standard Deviation = √(Variance)

Standard Deviation = √(2201000000)

Standard Deviation ≈ Rs. 46903.94