Consider a game that uses a 5-sided die. Each die is numbered 1-5 with an equal probability of rolling each number. The die is rolled 10 times, with each roll adding to the player's points. After 10 turns the points are added up.  Assume the CLT applies here. Which R code would calculate the chance of a player's points being between 25 and 35?单项选择题

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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

Regarding the Central Limit Theorem: Read the following statements. (a) Regardless of the underlying population distribution,  𝑋 ¯ is approximately Normal with mean 𝜇 and variance 𝜎 𝑛 . (b) Regardless of the underlying population distribution, 𝑌 = ∑ 𝑖 = 1 𝑛 𝑋 𝑖 is approximately distributed as 𝑁 ( 𝑛 𝜇 , 𝑛 𝜎 2 ) . (c) The central limit theorem can only be applied to continuous distributions. (d) If 𝑛 is greater than 25 or 30 then normal approximations generally will be good. Now choose the correct answer.    

Which of the following best describes the Central Limit Theorem in the context of a sampling distribution of the sample mean?

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