Sampling Distributions for Sample Proportions

AP Statistics· difficulty 3/5

p = 0.7, n = 100.

Approximately, what is P(p̂ < 0.65)?

  • A

    ≈ 0.5000

  • B

    ≈ 0.0668

  • C

    ≈ 0.0228

  • D

    ≈ 0.1379

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Explanation

σ_p̂ = √(0.7·0.3/100) ≈ 0.0458. z = (0.65−0.7)/0.0458 ≈ −1.09. P(Z < −1.09) ≈ 0.1379.

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