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A certain trial was done 200 times and the X event occurred 88 times. Find a...

A certain trial was done 200 times and the X event occurred 88 times. Find a 95% confidence interval for the true probability p of the event X.

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Answer #1

Sol:

p^=x/n=88/200= 0.44

zcrit for 95%=1.96

95% confidence interval for the true probability p of the event is

p^-Z*sqrt(p^*(1-p^)/n),p^+Z*sqrt(p^*(1-p^)/n)

0.44-1.96*sqrt(0.44*(1-0.44)/200),0.44+1.96*sqrt(0.44*(1-0.44)/200)

0.3712043, 0.5087957

95% confidence interval for p

(0.3712043, 0.5087957)

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