Question

A particular fruit's weights are normally distributed, with a mean of 320 grams and a standard deviation of 15 grams. If you pick 4 fruits at random, then 7% of the time, their mean weight will be above what value?

Answer 1

The mean weight of 4 fruits will be above 341.575 grams 7% of the time.

Step-by-step explanation:

To find the value above which the mean weight of 4 fruits will be 7% of the time, we need to find the corresponding z-score that corresponds to the upper 7% of the standard normal distribution.

This can be found using the standard normal distribution table or a calculator.

The z-score for an upper tail probability of 0.07 is approximately 1.405.

Next, we calculate the corresponding raw score using the formula:

x = mean + z * standard deviation

Substituting the values, we get:

x = 320 + 1.405 * 15 = 341.575 grams