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

Answer:

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