A charity receives 2025 contributions. Contributions are assumed to be mutually independent and identically distributed with mean 3125 and standard deviation 250.

Calculate the approximate 90th percentile for the distribution of the total contributions received.

• 6,328,000
• 6,338,000
• 6,343,000
• 6,784,000
• 6,977,000

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: C

The mean and standard deviation for the 2025 contributions are 2025(3125) = 6,328,125 and 45(250) = 11,250. By the central limit theorem, the total contributions are approximately normally distributed. The 90th percentile is the mean plus 1.282 standard deviations or 6,328,125 + 1.282(11,250) = 6,342,548.

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.