# Question: Given a population with mean 400 and variance

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 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?

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?

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