Financial Risk Manager Part 1

Explanation

To solve this problem, we need to find the percentage of the population with incomes between CAD 45,000 and CAD 50,000 using the normal distribution.

Step 1: Calculate Z-scores

• For CAD 45,000: $Z_1 = \frac{45,000 - 55,000}{10,000} = -1$

• For CAD 50,000: $Z_2 = \frac{50,000 - 55,000}{10,000} = -0.5$

Step 2: Find probabilities from Z-table

Using the standard normal distribution table:

• For Z = -1, the cumulative probability is 0.1587
• For Z = -0.5, the cumulative probability is 0.3085

Step 3: Calculate the probability between the two values

The percentage of population between CAD 45,000 and CAD 50,000 is: $P(45,000 < X < 50,000) = P(Z_2) - P(Z_1) = 0.3085 - 0.1587 = 0.1498$

This corresponds to 14.98% of the population.

Verification:

• The calculation is correct: 0.3085 - 0.1587 = 0.1498
• This represents the area under the normal curve between Z = -1 and Z = -0.5
• Option A (0.1498) is therefore the correct answer