SOLUTION: A particular fruit's weights are normally distributed, with a mean of 491 grams and a standard deviation of 9 grams.
If you pick 16 fruits at random, then 3% of the time, their
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Question 1184737: A particular fruit's weights are normally distributed, with a mean of 491 grams and a standard deviation of 9 grams.
If you pick 16 fruits at random, then 3% of the time, their mean weight will be greater than how many grams?
Give your answer to the nearest gram.
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
Since we are given that the weights are normally distributed with and ,
we want to solve for in the probability equation .
===> .
Now
===> ====> , or 495 grams to the nearest gram.
Therefore, if you pick 16 fruits at random, then 3% of the time, their mean weight will be greater than grams.
Note that, even though the sample size is < 30, we know by the CLT that the sampling distribution of the mean follows almost
a normal distribution whose parameters are known from the underlying population.
Probabilities were taken from https://stattrek.com/online-calculator/normal.aspx.
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