Given a population with mean 400 and variance 2 1, 600, the central limit theorem applies when the sample size is n 25 A random sample of size n 35 is obtained a What are the mean and variance of the sampling distribution for the sample means b What is the probability that x bar 412 c What is the probability that 393 x bar 407 d What is the probability that x bar 389

Question: Given a population with mean = 400 and variance 2 = 1, 600, the central limit theorem applies when the sample size is n

Given a population with mean μ = 400 and variance σ2 = 1, 600, the central limit theorem applies when the sample size is n ≥ 25. A random sample of size n = 35 is obtained.
a. What are the mean and variance of the sampling for the sample means?
b. What is the probability that x-bar > 412?
c. What is the probability that 393 ≤ x-bar ≤ 407?
d. What is the probability that x-bar ≤ 389?

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