Suppose a simple random sample of size n=50 is taken from a population of N=15,000 with a population proportion of p=0.4 having a certain characteristic. What is the probability that a simple random sample will have x > 21 having that characteristic?
(Round to four decimal places)
1
Expert's answer
2020-08-03T18:43:20-0400
Check that the sample size is large enough:
n⋅p=50⋅0.4=20≥10
np(1−p)=50⋅0.4(1−0.4)=12≥10
Sampling distribution for p^ is approximately normal:
μp^=p=0.4
σp^=np(1−p)=500.4(1−0.4)≈0.069282
5021=0.42
P(p^>0.42)=1−P(p^≤0.42)=
=1−P(Z≤0.0692820.42−0.4)≈1−P(Z≤0.288675)≈
≈0.386415
The probability that a simple random sample will have x > 21 having that characteristic is approximately 0.3864.
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