Question 194668
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?
<pre><font size = 4 color = "indigo"><b>
{{{mu=74}}},{{{sigma=8}}}

{{{drawing(400,200,-5,5,-.5,1.5, graph(400,200,-5,5,-.5,1.5, exp(-x^2/2)), 

line(-1.93,0,-1.93,exp(-1.93^2/2)),line(1.93,0,1.93,exp(-1.93^2/2))  
)}}}

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 + sigma*z}}}

For z = -1.96

{{{x = mu + sigma*z}}} 
{{{x = 74 + 8*(-1.96)}}}
{{{x = 58.32}}}

For z = +1.96

{{{x = mu + sigma*z}}} 
{{{x = 74 + 8*(1.96)}}}
{{{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</pre>