Question 733002
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Hello, please advise, having issues with this question.

The scores on a national test were normally distributed with a mean of 83 and a standard deviation of 8.  

If 400 test takers were selected at random, how many of them would you 
expect to have a score lower than 75?  (Round to the nearest person)
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<pre>
75 is one standard deviation below the mean:  75 = 83 - 8.


Use the empirical rule for the normal distribution:


    the area under the normal curve on the left of one standard deviation below the mean 

    is  0.5 - {{{0.68/2}}} = 0.5 - 0.34 = 0.16.


Therefore, the number of persons with the scores below 75 is  400*0.16 = 4*16 = 64.    <U>ANSWER</U>
</pre>

Solved.