Financial Risk Manager Part 1

Explanation:

To solve this problem, we need to calculate the probability that a randomly selected person from the population earns between CAD 45,000 and CAD 50,000, given a normal distribution with mean μ = CAD 55,000 and standard deviation σ = CAD 10,000.

Step 1: Calculate Z-scores

For the lower bound (CAD 45,000): $Z_1 = \frac{45,000 - 55,000}{10,000} = \frac{-10,000}{10,000} = -1$

For the upper bound (CAD 50,000): $Z_2 = \frac{50,000 - 55,000}{10,000} = \frac{-5,000}{10,000} = -0.5$

Step 2: Find probabilities from Z-table

Using the standard normal distribution table:

• For Z = -1, the cumulative probability (area to the left) is 0.1587
• For Z = -0.5, the cumulative probability (area to the left) is 0.3085

Step 3: Calculate the probability between the two bounds

The probability of earning between CAD 45,000 and CAD 50,000 is: $P(45,000 < X < 50,000) = P(Z < -0.5) - P(Z < -1) = 0.3085 - 0.1587 = 0.1498$

Step 4: Convert to percentage $0.1498 \times 100\% = 14.98\%$

Therefore, approximately 14.98% of the population earns between CAD 45,000 and CAD 50,000, which corresponds to option A (0.1498).