Shakeel Y.

asked • 09/27/17

mean weight of 800 people is 93kg and standard deviation of 4kg. how many people weigh under 89kg?

the answer given is 128, but how do they get to this?

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Kenneth S. answered • 09/27/17

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you want to find out the area under the standard normal distribution curve, corresponding to z = -1. 
That area is 0.15866; multiply this by 800 to obtain the requested answer.
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Kenneth S.

the result is 126.928, so since you cannot have fractional persons, the answer ought to be 126.
 
the quoted answer(128) may be the result of rounding errors attributed to using a lesser amount of accuracy (e.g. your table might give this area (or probability) just as 0.16).
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09/27/17

Shakeel Y.

thank you for your answer but i dont know where the z= -1 came from?
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09/28/17

Kenneth S.

z=0 corresponds to the mean; z=1 corresponds to 1 standard deviation above the mean; z=-1 corresponds to 1 standard deviation below the mean; the mean is 0 in the Standard Normal Distribution.
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09/28/17

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