:2. Solution. Since the box histogram follows the normal curve,
we can construct confidence intervals in the usual way, except
that we have to use the box SD+ instead of the box SD, and we use
the appropriate t-distribution instead of the normal curve.  The
sample average, 2, is the center of the confidence interval. <p>

 sample SD = 1+1/2 = 1     <p>

 SD+ = (2/1)^(1/2) x 1 = radical 2     <p>

 SE of the sum of the sample(figured using SD+) =     <p>

 radical 2 x radical 2 = 2     <p>

 SE of the sample average = SE of the sum/2     <p>

 = 2/2 = 1     <p>

The number of degrees of freedom is 2 - 1 = 1.  In The t-table on
page A-71, look for the "95%" column and the "2 degrees of
freedom" row.  They intersect at 12.71, so the  95% confidence
interval is <p>

 2  12.71x1 = 2  12.71,     <p>

so the "from -11 to 15" is the right choice. <p>

: if one takes a large number of samples
and constructs confidence intervals in the we just did, about 95%
of them will cover the box average. <p>