Sampling Distributions for Sample Proportions

AP Statistics· difficulty 3/5

p = 0.25, n = 400.

Approximately, what is P(p̂ > 0.30)?

A
$\approx 0.0228$
B
$\approx 0.1587$
C
$\approx 0.0104$
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D
$\approx 0.5000$

Explanation

σ_p̂ = \sqrt(0.25\cdot0.75/400) \approx 0.02165. z = 0.05/0.02165 \approx 2.31. P(Z > 2.31) \approx 0.0104.

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