For which of the following situations would the Central Limit Theorem for Sample Means APPLY?Select ALL correct answers:多项选择题
A
a. A random sample of size 50 is drawn from a bell-shaped population.
B
b. A random sample of size 50 is drawn from a skewed population.
C
c. A random sample of size 20 is drawn from a bell-shaped population.
D
d. A random sample of size 20 is drawn from a skewed population.
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"Why is the Central Limit Theorem so important anyway?" asks Quackers, somewhat irritated. "It seems too complex and abstract to be of any relevance to anything we actually care about." What would you tell him?
"Why is the Central Limit Theorem so important anyway?" asks Quackers, somewhat irritated. "It seems too complex and abstract to be of any relevance to anything we actually care about." What would you tell him?
The distribution of gestational times of zebra fish is skewed left with a mean of 6.5 days and standard deviation of 0.8 days. If we take repeated samples of size 50, we know the distribution of the sample mean is approximately normal here because of
Let X1, X2, … , X24 be independent observations from a random sample of size 24 from the uniform distribution 𝑈 ( 0 , 1 ) with pdf 𝑓 ( 𝑥 ) = 1 , and support 0 < 𝑥 < 1 . (a) The (1) mean, 𝜇 , of the uniform distribution, (2) variance, 𝜎 2 , of the uniform distribution, (3) mean, 𝜇 𝑋 ¯ , of the sampling distribution, and (4) variance, 𝜎 𝑋 ¯ 2 , of the sampling distribution are: (1) 1/2, (2) 1/12, (3) 1/2, (4) 1/288 (b) Using a normal approximation to find 𝑃 ( 1 / 2 ≤ 𝑋 ¯ ≤ 5 / 8 ) , the answer is: 0.483
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