The net profit from a certain investment is normally distributed with a mean of $10,000 and a standard deviation of $5,000. The probability that the investor will have a net loss is:
A) 0.4772
B) 0.9544
C) 0.0228
D) 0.9772
E) 1.0

Question

Quizplus · Accepted Answer

To find the probability of a net loss, we need to find the probability that the net profit is less than zero. We can standardize the distribution by subtracting the mean and dividing by the standard deviation to get a standard normal distribution.

Z = (0 - 10000) / 5000 = -2

Using a standard normal distribution table, we can find the probability of Z being less than -2:

P(Z < -2) = 0.0228

Therefore, the probability that the investor will have a net loss is 0.0228, or approximately 2.28%. Choice C is the correct answer.

The Net Profit from a Certain Investment Is Normally Distributed