# proportions and confidence intervals

**Question description**

In a random sample, 136 of 400 persons given a flu vaccine experienced some discomfort.

I was asked to set up a 95% confidence interval for the true proportion of persons who will experience some discomfort. The problem is solved by I need help with interpretation.

We have p = 0.34, n = 400, and z = 1.96 for 95%
confidence.

Interval = 0.34 ± 1.96√[(0.34)(0.66)/400]

= 0.34 ± 1.96√0.000561

= 0.34 ± 1.96(0.023685439)

=
(0.29357654, 0.38642346)

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