Question

particular fruit's weights are normally distributed, with a mean of 412 grams and a standard deviation of 28 grams. The heaviest 19% of frults weigh more than how many grams? Give your answer to the nearest whole gram.

Answer 1

To find the weight at which the heaviest 19% of fruits weigh more, you can use the z-score formula. In this case, the heaviest 19% of fruits weigh more than approximately 388 grams.

Step-by-step explanation:

To find the weight at which the heaviest 19% of fruits weigh more, we first need to find the z-score associated with the 19th percentile. From the given information, we know that the mean weight is 412 grams and the standard deviation is 28 grams.

Using the z-score formula: z = (x - mean) / standard deviation, we can rearrange it to find x, the weight at the 19th percentile.

Rearranging the formula gives us x = (z * standard deviation) + mean. We can find the z-score corresponding to the 19th percentile using a standard normal distribution table or a calculator.

Let's assume the z-score is -0.87. Plugging in the values, x = (-0.87 * 28) + 412, we get x ≈ 388 grams.

Therefore, the heaviest 19% of fruits weigh more than approximately 388 grams.