Question

A particular fruit's weights are normally distributed, with a mean of 581 grams and a standard deviation of 36 Brams. The heaviest 4% of fruits weigh more than how many grams? Give your answer to the nearest gram.

Answer 1

The heaviest 4% of the fruits weigh more than 644 grams, determined by using the z-score for the 96th percentile and the given mean and standard deviation.

Step-by-step explanation:

To find the weight above which the heaviest 4% of fruits lie, you need to look for the z-score that corresponds to the 96th percentile of the normal distribution (since 100% - 4% = 96%). Consulting the z-table or using statistical software, you'll find a z-score roughly around 1.75. You can then use the following formula to convert this z-score to the weight in grams:

Weight = Mean + (z-score × Standard Deviation)

Substituting the given mean and standard deviation:

Weight = 581 g + (1.75 × 36 g)

Weight = 581 g + 63 g

Weight = 644 grams (rounded to the nearest gram)

Therefore, the heaviest 4% of the fruit weigh more than 644 grams.