Explanation

To find the probability that X lies outside the range between 12 and 61, we need to calculate the probability that X < 12 or X > 61.

Step 1: Calculate z-scores

For X = 12: $z_1 = \frac{12 - 40}{14} = \frac{-28}{14} = -2$

For X = 61: $z_2 = \frac{61 - 40}{14} = \frac{21}{14} = 1.5$

Step 2: Find probabilities using standard normal distribution

• P(z < -2) = 0.0228
• P(z > 1.5) = 1 - P(z < 1.5) = 1 - 0.9332 = 0.0668

Step 3: Calculate total probability

Total probability = P(z < -2) + P(z > 1.5) = 0.0228 + 0.0668 = 0.0896

Converting to percentage: 0.0896 × 100% = 8.96%

Therefore, the probability that X lies outside the range between 12 and 61 is 8.96%.