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?Select one:a.0.0000.b.0.3413.c.0.0005.d.0.0500.e.0.5000.

To solve this problem, we need to use the concept of Z-score in statistics. The Z-score is a measure of how many standard deviations an element is from the mean.

Step 1: Identify the mean, standard deviation, and the value for which we need to find the probability. In this case, mean (μ) = $2500, standard deviation (σ) =$1000, and the value (X) = $2000.

Step 2: Calculate the Z-score using the formula Z = (X - μ) / σ. Substituting the given values, we get Z = (2000 - 2500) / 1000 = -0.5.

Step 3: Look up this Z-score in the Z-table to find the probability. The Z-table tells us what percentage of the data lies below (to the left of) our Z-score. For Z = -0.5, the value from the Z-table is 0.3085. This means that 30.85% of the data lies below $2000.

Step 4: However, we want to find the probability that the gain is at least $2000, which means we are interested in the area to the right of our Z-score. Since the total probability is 1, the probability that the gain is at least$2000 is 1 - 0.3085 = 0.6915.

So, the correct answer is not listed in the options. The probability that the investor’s net gain will be at least $2000 is approximately 0.6915 or 69.15%.

To solve this problem, we need to use the concept of Z-score in statistics. The Z-score is a measure of how many standard deviations an element is from the mean.

Step 1: Calculate the Z-score. The formula for the Z-score is:

Z = (X - μ) / σ

where: X is the value we are interested in, which is $2000 in this case. μ is the mean, which is$2500. σ is the standard deviation, which is $1000.

So, Z = (2000 - 2500) / 1000 = -0.5

Step 2: Look up this Z-score in the Z-table to find the probability. The Z-table tells us what percentage of the population is below a certain Z-score.

For Z = -0.5, the value from the Z-table is approximately 0.3085. This means that 30.85% of the time, the net gain will be less than $2000.

Step 3: However, we want to find the probability that the net gain will be at least $2000. So, we need to subtract the value we found from 1 (because the total probability is 1).

So, 1 - 0.3085 = 0.6915

Therefore, the probability that the investor’s net gain will be at least $2000 is approximately 0.6915 or 69.15%.

This option is not listed in the choices provided. There might be a mistake in the question or the provided choices.