According to the 2000 U.S. Census, 80% of Americans over the age of 25 have earned a high school diploma. Suppose we take a random sample of 120 Americans and record the proportion, p, of individuals in our sample that have a high school diploma.
Answers
Answer:
a) The mean is 0.8.
b) The standard deviation is 0.0365.
c) Normal
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
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]
80% of Americans over the age of 25 have earned a high school diploma.
This means that [tex]p = 0.8[/tex]
Suppose we take a random sample of 120 Americans
This means that [tex]n = 120[/tex].
Question a:
The mean is:
[tex]\mu = p = 0.8[/tex]
The mean is 0.8.
Question b:
The standard deviation is:
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.8*0.2}{120}} = 0.0365[/tex]
The standard deviation is 0.0365.
Question c:
By the Central Limit Theorem, approximately normal.
a) The mean is 0.8.
b) The standard deviation is 0.0365.
c) Normal
Here, we have,
we know that,
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean x and standard deviation σ, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean x and standard deviation s = σ/√n .
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean x=p and standard deviation s=√p(1-p)/n
80% of Americans over the age of 25 have earned a high school diploma.
This means that p=0.8
Suppose we take a random sample of 120 Americans
This means that n=120.
Question a:
The mean is:
x=p=0.8
The mean is 0.8.
Question b:
The standard deviation is:
s=0.0365
The standard deviation is 0.0365.
Question c:
By the Central Limit Theorem, approximately normal.
Learn more about standard deviation here:
brainly.com/question/23907081
#SPJ6
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Step-by-step explanation:
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Step-by-step explanation:
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Answers
Answer:
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Answers
Answer:
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Step-by-step explanation:
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