Answer:
1. Probability between 470 and 517 grams
Standardize the values:
Calculate the z-scores for the weight range:
Lower z-score = (470 grams - 490 grams) / 17 grams = -1.18
Upper z-score = (517 grams - 490 grams) / 17 grams = 1.60
2. Find the probability:
Use a standard normal table (or calculator function) to find the area between -1.18 and 1.60 under the standard normal curve.
Look up these z-scores in your standard normal table and subtract the two table values to find the total area.
For example, if the table shows an area of 0.8413 for 1.60 and 0.1151 for -1.18, then the probability is 0.8413 - 0.1151 = 0.7262.
This value represents the portion of the population (fruits) that fall within the weight range of 470 and 517 grams.
3. Heaviest 13%
(100% - 13%)
then, you can use a percentile table or a calculator function to find the z-score corresponding to the 87th percentile.
Multiply the z-score by the standard deviation (17 grams) and add the mean (490 grams) to get the weight that separates the heaviest 13%.
For example, if the 87th percentile's z-score is 1.30, then the weight threshold is (1.30 * 17 grams) + 490 grams = 511.1 grams (rounded to one decimal place).
Therefore, the heaviest 13% of fruits weigh more than 511.1 grams.
Step-by-step explanation:
