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's net gain will be at least $2,000 is most closely reflected by _____________.
A)0.0000
B)0.3413
C)0.6915
D)0.0500
E)0.5000

Question

Quizplus · Accepted Answer

To find the probability that the investor's net gain will be at least $2,000, we calculate the Z-score for $2,000 and then find the corresponding probability from the normal distribution. The Z-score is calculated as $Z = \frac{(X - \mu)}{\sigma}$, where $X$ is the value of interest ($2,000), $\mu$ is the mean ($2,500), and $\sigma$ is the standard deviation ($1,000). Plugging in the values, we get $Z = \frac{(2000 - 2500)}{1000} = -0.5$. Looking up the Z-score of -0.5 in a standard normal distribution table or using a calculator, we find that the probability of being less than $2,000 is approximately 0.3085. However, we are interested in the probability of being at least $2,000, which is 1 - 0.3085 = 0.6915. Therefore, the closest choice is 0.6915.

The Net Profit from a Certain Investment Is Normally Distributed