Question 1192816
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n = 650 = sample size
x = 117 = number of falls
phat = x/n = 117/650 = 0.18


At 99% confidence, we have z = 2.576 as the approximate critical value. 
This value is used often in confidence intervals that you should memorize it, or have it handy on a reference table.


E = margin of error
E = z*sqrt(phat*(1-phat)/n)
E = 2.576*sqrt(0.18*(1-0.18)/650)
E = 0.03881792879981
E = 0.0388 
which is approximate


L = lower boundary
L = phat - E
L = 0.18 - 0.0388
L = 0.1412


U = upper boundary
U = phat + E
U = 0.18 + 0.0388
U = 0.2188



Answer: <font color=red>(0.1412, 0.2188)</font>
The boundary values are approximate because the value of E was approximate. Round however instructed.


An alternative way to express the confidence interval is to write  0.1412 < p < 0.2188
This shows that we're 99% confident the population proportion (p) is somewhere between 0.1412 and 0.2188
In other words, we're 99% confident the population percentage is between roughly 14.12% and roughly 21.88%
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