Question

A retail ice cream salesman divides his working days into 'sunny', 'medium', and 'cold'. He estimates that the probability of it being sunny is 0.2, and cold 0.3. If his gross sales on these three types of day are $50, $35, and $10 respectively on average and his average daily costs are $18 on any day.

Required:
a. Complete the probability distribution.
b. Find his expected profit per day.

Answer 1

a. The probability distribution is Sunny: 0.2, Medium: 0.5, Cold: 0.3. b. The expected profit per day is 10.

Step-by-step explanation:

a. To complete the probability distribution, we need to calculate the probability of it being 'medium'. Since the probabilities of sunny and cold days are already given as 0.2 and 0.3 respectively, the probability of a 'medium' day can be found by subtracting the sum of these probabilities from 1:

P(medium) = 1 - P(sunny) - P(cold) = 1 - 0.2 - 0.3 = 0.5

So, the probability distribution is as follows:

Sunny: 0.2

Medium: 0.5

Cold: 0.3

b. To find the expected profit per day, we need to multiply the sales and costs by their corresponding probabilities and sum them up.

Expected profit per day = (Sales(sunny) * P(sunny)) + (Sales(medium) * P(medium)) + (Sales(cold) * P(cold)) - Costs = (50 * 0.2) + (35 * 0.5) + (10 * 0.3) - 18 = 10

Answer 2

30.5

Step-by-step explanation:

Let ;

Sunny = S ; Medium = M ; Cold = C

_____ S _____ M ___ C

__X : 50 ____ 35 ___ 10

P(X) : 0.2 ____ 0.5 __ 0.3

P(M) = 1 - (0.2 + 0.3)

P(M) = 1 - 0.5 = 0.5

Expected profit per day, E(X)

E(X) = sum of (X * p(x)

E(X) = (50 * 0.2) + (35 * 0.5) + (10 * 0.3)

E(X) = 10 + 17.5 + 3

E(X) = 30.5