Th average mass of an avocado sold by the shop is 200 g with a st. ndard deviation of 15 g Asme the mass of avocadoes sold by the shop is normally dilutibuted. (6) What percentage of avocadoes are between 175 g and 220 g ? (A

To find the percentage of avocados that weigh between 175 g and 220 g, we can use the properties of the normal distribution. Given that the average mass (mean) of the avocados is 200 g and the standard deviation is 15 g, we can standardize the values using the z-score formula: \[ z = \frac{(X - \mu)}{\sigma} \] where: - \(X\) is the value we are standardizing, - \(\mu\) is the mean, - \(\sigma\) is the standard deviation. ### Step 1: Calculate the z-scores 1. For 175 g: \[ z_{175} = \frac{(175 - 200)}{15} = \frac{-25}{15} \approx -1.67 \] 2. For 220 g: \[ z_{220} = \frac{(220 - 200)}{15} = \frac{20}{15} \approx 1.33 \] ### Step 2: Use the z-scores to find the corresponding probabilities Next, we can look up these z-scores in the standard normal distribution table or use a calculator to find the probabilities. - For \(z = -1.67\), the cumulative probability (area to the left) is approximately 0.0478. - For \(z = 1.33\), the cumulative probability is approximately 0.9082. ### Step 3: Calculate the percentage of avocados between 175 g and 220 g To find the percentage of avocados between these two weights, we subtract the cumulative probability at \(z = -1.67\) from the cumulative probability at \(z = 1.33\): \[ P(175 < X < 220) = P(Z < 1.33) - P(Z < -1.67) \approx 0.9082 - 0.0478 = 0.8604 \] ### Step 4: Convert to percentage To convert this probability to a percentage, we multiply by 100: \[ 0.8604 \times 100 \approx 86.04\% \] ### Conclusion Approximately **86.04%** of the avocados sold by the shop weigh between 175 g and 220 g.