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 not have a net loss is ___.
A)0.4772
B)0.0228
C)0.9544
D)0.9772
E)1.0000

Question

Quizplus · Accepted Answer

To not have a net loss means that the net profit is greater than or equal to $0. We can standardize this by subtracting the mean and dividing by the standard deviation: (0 - 10000)/5000 = -2. The probability of a z-score being less than -2 is approximately 0.0228, which is the probability that the investor will have a net loss. Therefore, the probability that the investor will not have a net loss is 1 - 0.0228 = 0.9772, which is answer choice D.

The Net Profit from a Certain Investment Is Normally Distributed