Question

The monthly profit of a sticker selling business, in thousands of dollars, has a normal distribution with variance equal to the cube of its mean. The probability the business does not make a profit for the month is 10%.

Calculate the expected monthly profit.

Answer 1

To calculate the expected monthly profit, we need to find the mean of the normal distribution. The probability of the business not making a profit is 10%, so the probability of making a profit is 0.90. The expected monthly profit can be calculated by multiplying each profit value by its corresponding probability and summing them up.

Step-by-step explanation:

To calculate the expected monthly profit, we need to find the mean of the normal distribution. Let's denote the mean as x and the variance as x^3. We know that the probability of the business not making a profit is 10%, so the probability of making a profit is 1 - 0.10 = 0.90.

Since the total probability must equal 1, the probability of making a profit is divided equally among all profit values. Let's denote the profit value as p. Therefore, the probability of making a profit of p is 0.90 divided by the number of profit values.

The expected monthly profit can be calculated by multiplying each profit value by its corresponding probability and summing them up. So, the expected monthly profit is:

E(x) = 0(p1) + 1(p2) + 2(p3) + ... + x(p(x+1))

where p1, p2, p3, ... are the probabilities of each profit value.