Question

A particular fruit's weights are normally distributed, with a mean of 651 grams and a standard deviation of 27 grams. if you pick 49 fruit at random, what is the probability that their mean weight will be between 642 grams and 657 grams

Answer 1

Answer: About 21.64% of the fruit will be between 642 and 657 grams.

To solve this problem, we will have to find the probability for each z-score on the normal distribution. Then, subtract them to find the difference.

Lower End:
-9/27 = -0.33 for the z-score which is a probability of 0.3707

Upper End: 
6/27 = 0.22 for the z-score which is a probability of 0.5871.

0.5871 - 0.3707 = 0.2164

Or about 21.64%