Mathematics
The Sample Proportion

### Question Description

Suppose that 29% of all residents of a community favor annexation by a nearby municipality. Find the probability that in a random sample of 50 residents at least 35% will favor annexation

Standard deviation of a proportion p is given by sqrt(p(1-p))

sd = sqrt(0.29 x 0.71)

= 0.4538

So the standard error for a sample mean is given by sd/sqrt(n) where n is the sample size:

SEM = sd/sqrt(n)

= 0.4538/sqrt(50)

0.0642

So the probability that fewer than 35% favor annexation is the normal cdf at .35 with mean = .29 and sd = SEM = 0.0642:

Norm.cdf (sample mean, population mean, standard error)

= Norm.cdf (0.35, 0.29, 0.0642)

0.825

So the probability that more than 35% favor annexation is 1-0.825 = 0.175.

iainharlow (1041)
University of Virginia
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