Sampling Distributions for Sample Proportions

AP Statistics· difficulty 2/5

A random sample of n = 60 households is taken; the true proportion that own a pet is p = 0.55.

Check Large Counts np = 60(0.55) = 33 n(1-p) = 60(0.45) = 27 Both ≥ 10 ✓

Is Large Counts satisfied?

  • A

    Yes, because np = 33 and n(1-p) = 27, both ≥ 10.

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  • B

    Yes, because n > 30.

  • C

    No, because p > 0.5.

  • D

    No, because n < 100.

Explanation

np = 33 ≥ 10 and n(1−p) = 27 ≥ 10, so Large Counts is satisfied.

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