To solve part (i) of the problem, let's follow these steps: Given data: - Mean (\( \mu \)) = 55 months - Standard deviation (\( \sigma \)) = 10 months (i) Sketch an accurate normal distribution curve labeled correctly with the 68-95-99.7 rule: 1. **Calculate the intervals using the 68-95-99.7 rule:** - 68% of the data lies within \( \mu \pm \sigma \) - 95% of the data lies within \( \mu \pm 2\sigma \) - 99.7% of the data lies within \( \mu \pm 3\sigma \) Therefore, for our problem: - 68% of the autos have service months between \( 55 - 10 = 45 \) months and \( 55 + 10 = 65 \) months. - 95% of the autos have service months between \( 55 - 2 \times 10 = 35 \) months and \( 55 + 2 \times 10 = 75 \) months. - 99.7% of the autos have service months between \( 55 - 3 \times 10 = 25 \) months and \( 55 + 3 \times 10 = 85 \) months. 2. **Sketch the normal distribution curve:** - Center the curve at \( \mu = 55 \). - Mark \( \mu - \sigma =