**10. Correct. The answer is true.**

Let X_{i} 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*N^{0.5}.
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%.