SOLUTION: A particular fruit's weights are normally distributed, with a mean of 453 grams and a standard deviation of 18 grams. If you pick 19 fruits at random, then 7% of the time, their

Question 1147747: A particular fruit's weights are normally distributed, with a mean of 453 grams and a standard deviation of 18 grams.
If you pick 19 fruits at random, then 7% of the time, their mean weight will be greater than how many grams?
Give your answer to the nearest gram.
Answer by VFBundy(438) (Show Source): You can put this solution on YOUR website!
First, you want to find the standard deviation of the sample. You do this by taking the standard deviation of the population and dividing it by the square root of the number of items in the sample:

= 18/4.3589 = 4.1295

Since you want to find the number of years where the mean weight is in the highest 7%, you want to go to a z-table and find the z-score that where the area to the left of the curve is closest to 0.93. (Because this is also the z-score where the area that is to the right of the curve is 0.07.) The z-score that is closest is 1.48.
Now, you want to set up an equation as such:

x - 453 = 1.48(4.1295)

x - 453 = 6.1117

x = 459.1117

Rounded off to the nearest gram, the answer is 459 grams.
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