Question

Question 3

An Italian Ice (snowcone) retailer is examining his profits for the spring season of the previous year. He realizes that his sales are based on the daily weather: sunny, average, or cold. He estimates that this year the probability of it being sunny is 0.2, average 0.5, and cold 0.3. His gross sales on these three types of days average $50, $35, and $10 respectively.

a. Find the expected income in any one day.
b. If the average supplies cost $18, what is the expected daily profit?

Answer 1

Answer on Question #83657 – Math – Statistics and Probability

Question

An Italian Ice (snowcone) retailer is examining his profits for the spring season of the previous year. He realizes that his sales are based on the daily weather: sunny, average, or cold. He estimates that this year the probability of it being sunny is 0.2, average 0.5, and cold 0.3. His gross sales on these three types of days average $50, $35, and $10 respectively.

a. Find the expected income in any one day.

b. If the average supplies cost $18, what is the expected daily profit?

Solution

a. Expected income in any one day can be calculated by using the following formula:

$$\sum_{i=1}^{n} P_i * R_i$$

, where $P_i$ is the probability for the return $R_i$, and $n$ is the number of scenarios. In this case expected income can be calculated as:

$$0.2 * 50 + 0.5 * 35 + 0.3 * 10 = 10 + 17.5 + 3 = 30.5$$

b. If the average supplies cost $18, the expected daily profit is expected daily income minus average supply. It is $30.5 - 18 = 12.5$

Answer:

a. The expected income in any one day is $30.5.

b. The expected daily profit is $12.5.

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