The net profit from a certain investment is normally distributed with a mean of $2,500 and a standard deviation of $1,000.The probability that the investor will not have a net loss is _____________.
A)0.4938
B)0.0062
C)0.9938
D)0.5062
E)0.0000

Question

Quizplus · Accepted Answer

To find the probability that the investor will not have a net loss, we need to calculate the probability that the net profit is greater than or equal to $0. Using the Z-score formula, Z = (X - μ) / σ, where X is the value of interest ($0 in this case), μ is the mean ($2,500), and σ is the standard deviation ($1,000), we find Z = (0 - 2500) / 1000 = -2.5. Looking up the Z-score of -2.5 in the standard normal distribution table or using a calculator, we find that the probability of having a value less than -2.5 is approximately 0.0062. Therefore, the probability of not having a net loss (or having a net profit) is 1 - 0.0062 = 0.9938.

The Net Profit from a Certain Investment Is Normally Distributed