A particular fruit's weights are normally distributed, with a mean of 618 grams and a standard deviation of 24 grams. If you pick 2 fruit at random, what is the probability that their mean weight will be between 568 grams and 616 grams

Question

Kathryn Dickerson

Mathematics

6 July, 23:29

A particular fruit's weights are normally distributed, with a mean of 618 grams and a standard deviation of 24 grams. If you pick 2 fruit at random, what is the probability that their mean weight will be between 568 grams and 616 grams

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Claudia Wilcox · Answer 1

Answer: The probability is 0.5136.

To find this probability we have to find the range of the values on the normal distribution table.

First, we need to find the percent for each making z-score.

Lower end: 50/24 = 2.08 = 0.0183

Upper end: 2/24 = 0.08 = 0.5319

Now, that we have the upper and lower ends, we can subtract them to find the difference or the range.

0.5319 - 0.0183 = 0.5136

There is a 51.36% chance they are in the given range.