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Answer: 0.1498
**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).
Author: Nikitesh Somanthe
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The population living in Calgary, Canada has a mean income of CAD 55,000 with a standard deviation of CAD 10,000. If the distribution is assumed to be normal, what is the percentage of the population that makes between CAD 45,000 and CAD 50,000?
A
0.1498
B
0.1511
C
0.1624
D
0.2014