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Sagot :
Answer:
The mean of the sampling distribution of p is 0.75 and the standard deviation is 0.0306.
Step-by-step explanation:
Central Limit Theorem:
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
75% of teenagers in North America are pursuing a goal they have set for themselves.
This means that [tex]p = 0.75[/tex]
Sample of 200.
This means that [tex]n = 200[/tex].
What are the mean and standard deviation of the sampling distribution of p?
By the Central Limit Theorem
Mean [tex]\mu = p = 0.75[/tex]
Standard deviation [tex]s = \sqrt{\frac{0.75*0.25}{200}} = 0.0306[/tex]
The mean of the sampling distribution of p is 0.75 and the standard deviation is 0.0306.
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