# If n=590 and p=0.93, construct a 90\% confidence interval.

If $n=590$ and $p=0.93$, construct a $90\mathrm{%}$ confidence interval.
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Step 1
Express the expression for the confidence interval.
$C.I=p±Z\cdot \sqrt{\frac{p\left(1-p\right)}{n}}$
Here, Z* is the critical value .
From the Z table, the value corresponding to the region 90.5 is,
$Z\cdot =1.31$
Step 2
Put 590 for n, 0.93 for p, 1.31 for Z* implies,
$C.I=0.93±1.31\sqrt{\frac{0.93\left(1-0.93\right)}{0.93}}$
$C.I=0.93±0.346$
Thus, the confidence interval is $0.93+0.346$ and $0.93-0.346$.