Sampling Distributions for Sample Proportions

AP Statistics· difficulty 2/5

A polling firm samples n = 50 adults to estimate the proportion p who use a particular app, where p = 0.10.

Large Counts: np ≥ 10, n(1-p) ≥ 10 np = 50(0.10) = 5 n(1-p) = 45 5 < 10 → fails

Is the Large Counts condition satisfied?

  • A

    Yes, because both np and n(1-p) are positive.

  • B

    No, because np = 5 < 10.

    check_circle
  • C

    No, because p < 0.5.

  • D

    Yes, because n = 50 ≥ 30.

Explanation

Large Counts requires np ≥ 10 and n(1-p) ≥ 10. Here np = 50(0.10) = 5 < 10, so the condition fails.

Want 10 more like this — adaptive to your weak spots?

Related questions