Final answer:
The probability that the sum of the two observations is greater than 221 is approximately 2.41%.
Step-by-step explanation:
To find the probability that the sum of the two observations is greater than 221, we can use the properties of normal distribution.
The sum of two normally distributed variables is also normally distributed.
Given that the mean of the population is 100 and the standard deviation is 5, we know that the sum of two random samples will follow a normal distribution with a mean of 200 (2 * 100) and a standard deviation of
√(2 * 5^2) = √(50)
≈ 7.07.
To find the probability, we need to find the area under the curve to the right of 221.
Using a standard normal distribution table or a calculator, we can find that the probability is approximately 0.0241, or 2.41%.