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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.

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.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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### Understanding Normal Distribution of Fruit Weights A 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**.
Transcribed Image Text:### Understanding Normal Distribution of Fruit Weights A 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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