Sampling Distributions for Sample Proportions

AP Statistics· difficulty 3/5

p = 0.20, n = 100.

Approximately, what is P(p̂ < 0.15)?

  • A

    0.2500

  • B

    0.0500

  • C

    0.1056

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  • D

    0.4013

Explanation

σ_p̂ = √(0.2·0.8/100) = 0.04. z = (0.15−0.20)/0.04 = −1.25. P(Z < −1.25) ≈ 0.1056.

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