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

Question

Kody Griffith

Mathematics

28 October, 15:15

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

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Answers (1)

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Jacqueline Casey · 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%