SOLUTION: A baking company sells cakes by weight. The demand for cakes, on a day varies in a uniform manner between 2000 kgs and 3000 kgs. Further, he finds the distribution of profit as g

Question 1192502: A baking company sells cakes by weight. The demand for cakes, on a day varies in a
uniform manner between 2000 kgs and 3000 kgs. Further, he finds the distribution of profit as given below
Daily demand(in Kgs) -- Average profit
2000-2250 -- 981.5
2250-2500 -- 1136.5
2500-3000 -- 1344.2
Calculate the probability that on a randomly selected day the demand lies between
(i) 2000-2250 kgs, (ii) 2250- 2500 kgs (iii) 2500- 3000 kgs, hence obtaining the expected profit on a randomly chosen day
Answer by CPhill(1987) (Show Source): You can put this solution on YOUR website!
**1. Calculate the Probability of Each Demand Range**
* **Total Range of Demand:** 3000 kgs - 2000 kgs = 1000 kgs
* **Probability of Demand between 2000-2250 kgs:**
(2250 kgs - 2000 kgs) / 1000 kgs = 250 kgs / 1000 kgs = 0.25
* **Probability of Demand between 2250-2500 kgs:**
(2500 kgs - 2250 kgs) / 1000 kgs = 250 kgs / 1000 kgs = 0.25
* **Probability of Demand between 2500-3000 kgs:**
(3000 kgs - 2500 kgs) / 1000 kgs = 500 kgs / 1000 kgs = 0.50
**2. Calculate the Expected Profit**
* **Expected Profit:**
(Probability of Range 1 * Average Profit of Range 1) +
(Probability of Range 2 * Average Profit of Range 2) +
(Probability of Range 3 * Average Profit of Range 3)
= (0.25 * 981.5) + (0.25 * 1136.5) + (0.50 * 1344.2)
= 245.375 + 284.125 + 672.1
= **1201.6**
**Therefore:**
* The probability of demand between 2000-2250 kgs is 0.25.
* The probability of demand between 2250-2500 kgs is 0.25.
* The probability of demand between 2500-3000 kgs is 0.50.
* The expected profit on a randomly chosen day is $1201.60.

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