SOLUTION: The birth weights for twins are normally distributed with a mean of 2353 grams and a standard deviation of 647 grams. Use z-scores to determine which birth weight could be consider

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Question 69161This question is from textbook Elementary Statistics
: The birth weights for twins are normally distributed with a mean of 2353 grams and a standard deviation of 647 grams. Use z-scores to determine which birth weight could be considered unusual. This question is from textbook Elementary Statistics

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The birth weights for twins are normally distributed with a mean of 2353 grams and a standard deviation of 647 grams. Use z-scores to determine which birth weight could be considered unusual.
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Most texts use 2 standard deviations as the boundary for usual
verses unusual.
If you convert your mean to a z-score it is 0.
You are looking for the raw score that corresponds to
z= 2 of z=-2
The formula that relates z and x (x is the usual symbol for raw scores) is:
z=(x-u)/sigma
So letting z=2 you get:
2=(x-2353)/647
x-2353=2*647
x=2353+2*647
x=3647
This is the raw score (birth weight) that is 2 standard deviations above the mean.
Then let z=-2
-2=(x-2353)/647
x-2353=-2*647
x=1059
This score is 2 standard deviations below the mean.
Cheers,
Stan H.