The population proportion is .50 . What is the probability that a sample proportion will be within +/- .04 of the population proportion for each of the following sample sizes? Round your answers to 4 decimal places. Use z-table.
a. n= 100
b .n= 200
c. n= 500
d. n= 1000
Z = (p^- p )/sqrt(pq/n) = (p^- p)/sqrt(0.5 * 0.5/n)
a)
P( -0.04 < p^- p < 0.04)
= P(|Z| < 0.04/sqrt(0.5 * 0.5/n))
=P(|Z| < sqrt(n) * 0.04/0.5)
= P(|Z| < 0.08 * sqrt(n))
Now
n = 100
P(|Z| < 0.8)
=
P (−0.8<Z<0.8 )=0.5762
b) n = 200
P(|Z| < 1.131370 )
=
P (−1.131370<Z<1.131370 )=0.7416
c)
n = 500
P(|Z| < 1.788854 )
=
P (−1.788854<Z<1.788854 )=0.9266
d)
n = 1000
P(|Z| < 2.529822 )
=
P (−2.529822<Z<2.529822 )=0.9886
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