Solved – wrong with these statements?

Explain what is wrong in each of the following statements.

(a) For large sample size n, the distribution of observed values will be approximately Normal.

(b) The 68-95-99.7 rule says that $bar x$ should be within µ ± 2σ about 95% of the time.

(c) The central limit theorem states that for large n, µ is approximately Normal.

(a) For a large sample size, the distribution of observed values will be approximately the actual underlying distribution of the random process. If they come from a normal distribution, it'll look normal. If they comes from a uniform distribution, it'll look uniform.

(b) According to the 68-95-99.7 rule, the sample average should be within $mupm2frac{sigma}{sqrt{n}}$ about 95% of the time. Note that as $n$, the number of samples, goes up, the sample average is contained in a closer and closer ball to the theoretical average.

(c) The sample average of $n$ values will be approximately normally distributed. The sample average, or observed average, is often called $hat{mu}$. However, if you knew the actual distribution, then $mu$, the theoretical average or expectation of the distribution, is a fixed, non-random number that is a property of the distribution.

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