SOLUTION: 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

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Question 733002: 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)
Found 2 solutions by lynnlo, ikleyn:
Answer by lynnlo(4176) About Me  (Show Source):
Answer by ikleyn(53763) About Me  (Show Source):
You can put this solution on YOUR website!
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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)
~~~~~~~~~~~~~~~~~~~~~~~~~~ 

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%2F2 = 0.5 - 0.34 = 0.16.


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

Solved.