For which of the following sample sizes would the sampling distribution of p̂ be approximately normal when p = 3
(Select all that apply.)
n = 10
n = 25
n = 50
n = 100
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To determine if the sampling distribution of p̂ is approximately normal, we need to check if both np and n(1-p) are greater than or equal to 10.
Given that p = 3, we can calculate np and n(1-p) for each sample size.
n = 10:
np = 10 * 3 = 30
n(1-p) = 10 * (1-3) = 10 * (-2) = -20
Since n(1-p) is not greater than or equal to 10, the sampling distribution of p̂ is not approximately normal for n = 10.
n = 25:
np = 25 * 3 = 75
n(1-p) = 25 * (1-3) = 25 * (-2) = -50
Since n(1-p) is not greater than or equal to 10, the sampling distribution of p̂ is not approximately normal for n = 25.
n = 50:
np = 50 * 3 = 150
n(1-p) = 50 * (1-3) = 50 * (-2) = -100
Since n(1-p) is not greater than or equal to 10, the sampling distribution of p̂ is not approximately normal for n = 50.
n = 100:
np = 100 * 3 = 300
n(1-p) = 100 * (1-3) = 100 * (-2) = -200
Since np is greater than or equal to 10 and n(1-p) is greater than or equal to 10, the sampling distribution of p̂ is approximately normal for n = 100.
Therefore, the sample size for which the sampling distribution of p̂ is approximately normal is n = 100.
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