SOLUTION: a set of test scores is normally distributed with a mean of 74 and a standard deviation of 8. Between what two scores does the middle 95% of the data fall?

Algebra ->  Probability-and-statistics -> SOLUTION: a set of test scores is normally distributed with a mean of 74 and a standard deviation of 8. Between what two scores does the middle 95% of the data fall?      Log On


   

Question 194668This question is from textbook Saxon Algebra 2
: a set of test scores is normally distributed with a mean of 74 and a standard deviation of 8. Between what two scores does the middle 95% of the data fall? This question is from textbook Saxon Algebra 2

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
a set of test scores is normally distributed with a mean of 74 and a standard deviation of 8. Between what two scores does the middle 95% of the data fall?

mu=74,sigma=8



From the table we get that .025 of 2.5% of the data lies to the
left of z=-1.96, and .025 or 2.5% of the data lies to the
right of z=+1.96

To find the two x values that corresponds to z=-1.96 and z=+1.96  
we use the formula:

x+=+mu+%2B+sigma%2Az

For z = -1.96

x+=+mu+%2B+sigma%2Az 
x+=+74+%2B+8%2A%28-1.96%29
x+=+58.32

For z = +1.96

x+=+mu+%2B+sigma%2Az 
x+=+74+%2B+8%2A%281.96%29
x+=+89.68

So the middle 95% of the scores lie between 
58.32 and 89.68.  Maybe you'd round those and
make it between 58 and 90.

Edwin