### Understanding Normal Distribution of Fruit WeightsA particular fruit's weights are normally distributed, with a mean of 579 grams and a standard deviation of 10 grams.**Problem:**The heaviest 14% of fruits weigh more than how many grams?Give your answer to the nearest gram.---**Solution:**To find this value, we need to determine the z-score for the top 14% of the distribution. The z-score can be found in z-tables or calculated using statistical software or calculators. Once the z-score is determined, we can then convert it to the actual weight using the mean and standard deviation provided.1. **Determine the z-score for the top 14%:** - The area to the left of the z-score that corresponds to the top 14% is 1 - 0.14 = 0.86. - Using a z-table or statistical software, find the z-score that corresponds to 0.86.2. **Calculate the corresponding weight:** - Use the formula: \( W = \mu + z \cdot \sigma \) where \( W \) is the weight, \( \mu \) is the mean (579 grams), and \( \sigma \) is the standard deviation (10 grams).3. **Substitute the values:** - Find the z-score for 0.86 (which is approximately 1.08). - \( W = 579 + (1.08 \times 10) \). - \( W = 579 + 10.8 \). - \( W = 589.8 \).Rounded to the nearest gram, the weight is approximately **590 grams**.Therefore, the heaviest 14% of fruits weigh more than **590 grams**.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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A particular fruit's weights are normally distributed, with a mean of 579 grams and a standard deviation of 10 grams. The heaviest 14% of fruits weigh more than how many grams? Give answer to the nearest gram.