10. Incorrect. The answer is true, not false.
Let Xi be the random value of each individual claim 'i'. Because the values are independent random variables, the sum of the values of the individual claims will be normally distributed according to the Central Limit Theorem:
Total Value of Claims is
where the mean is μ = 500000*N and the standard deviation is σ = 100000*N0.5. If N = 55, then μ = $27,500,000 and σ = $741,619.85. In order to calculate the requested probability, first you have to standardize S = $29,000,000
Z = (29,000,000 – 27,500,000) / (741,619.85) = 2.0226
Using the standard normal distribution table, you can calculate the requested probability as follows:
P[Z > 2.0226] = (area to the right of z = 2.0226) = (area to the right of z = 0) – (area between z = 0 and z = 2.0226) = P[Z > 0] – P[0 ≤ Z ≤ 2.0226] = 0.5 – 0.4783 ≈ 0.0217 or 2.17%.