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19 September, 14:20

Suppose we select a simple random sample of size n=250 from a large population with a proportion p of successes. Let p be the proportion of successes in the sample. For which value of p is it appropriate to use the normal approximation for the sampling distribution of p?

A. 0.03

B. 0.15

C. 0.02

D. 0.97

E. 0.99

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  1. 19 September, 14:36
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    B. 0.15

    Step-by-step explanation:

    To approximate a binomial distribution as a normal distribution, two conditions must be met:

    np > 10

    nq = n (1-p) > 10

    Here, n = 250. Check each value of p to see if it meets the conditions.

    A. p = 0.03

    np = 7.5, nq = 242.5

    B. p = 0.15

    np = 37.5, nq = 212.5

    C. p = 0.02

    np = 5, nq = 245

    D. p = 0.97

    np = 242.5, nq = 7.5

    E. p = 0.99

    np = 247.5, nq = 2.5

    Of the five choices, only B meets both conditions.
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