1. Approximately 0.14% of hedge fund investors have incomes less than $100,000.
2. The area greater than 2.00 is 1 - 0.97725 = 0.02275.
3. The area greater than -1.00 is 1 - 0.15865 = 0.84135.
1. What percent of hedge fund investors have incomes less than $100,000?
To calculate the percentage of hedge fund investors with incomes less than $100,000, we need to find the z-score of $100,000 and then use the standard normal distribution table to find the corresponding area.
z = (X - μ) / σ = ($100,000 - $175,000) / $25,000 = -3.00
Using the standard normal distribution table, we find that the area less than -3.00 is 0.00135. Therefore, approximately 0.14% of hedge fund investors have incomes less than $100,000.
2. What percent of hedge fund investors have incomes greater than $225,000?
To calculate the percentage of hedge fund investors with incomes greater than $225,000, we need to find the z-score of $225,000 and then subtract the area less than that z-score from 1 (which represents the total area under the standard normal distribution curve).
z = (X - μ) / σ = ($225,000 - $175,000) / $25,000 = 2.00
Using the standard normal distribution table, we find that the area less than 2.00 is 0.97725. Therefore, the area greater than 2.00 is 1 - 0.97725 = 0.02275. This means that approximately 2.28% of hedge fund investors have incomes greater than $225,000.
3. What percent of hedge fund investors have incomes greater than $150,000?
To calculate the percentage of hedge fund investors with incomes greater than $150,000, we need to find the z-score of $150,000 and then subtract the area less than that z-score from 1 (which represents the total area under the standard normal distribution curve).
z = (X - μ) / σ = ($150,000 - $175,000) / $25,000 = -1.00
Using the standard normal distribution table, we find that the area less than -1.00 is 0.15865. Therefore, the area greater than -1.00 is 1 - 0.15865 = 0.84135. This means that approximately 84.14% of hedge fund investors have incomes greater than $150,000.