he heaviest 4% of fruits weigh more than how many grams?

Question

A particular fruit's weights are normally distributed, with a mean of 715 grams and a standard deviation of 14 grams.

The heaviest 4% of fruits weigh more than how many grams?

Give your answer to the nearest gram.

Answer 1

To calculate the heaviest 4% of fruits weigh how many grams, you need to know a few pieces of information.

1. Is this distribution normal?
2. Yes it is! This means we can use a standard unimodal model to calculate using a couple key metrics
3. The mean
4. As described, it is 715 grams. This gives us a starting point for our calculation as we know what weight the 50% heaviest fruits are, because the mean = 50th percentile
5. The standard deviation
6. As described, it is 14 grams. This measure tells us for all fruits, what is the average distance its weight is from the mean of 715 grams?

Using these pieces of information, we can then calculate the answer by using a simple z score formula and z score table.

We know a z score is z = (x - μ) / σ (x minus the mean divided by the standard deviation).

What we want is the x. We want to know what weight the 4% is at. So, we need to reverse-look up a z score to plug it into the formula. Looking at a z-score table, you want to look in the values to find .9600 (or as close to it as possible) and look at the column/row to see what z score that is.

Then you plug that into the formula above.

your z score = (x - 715) / 14

Then, simply solve for x and you have your answer!

Do not forget to round to the nearest gram as the question requested.