Let x1xnnbspbe an iid sample from a population with unknown

Question

Let X₁,...,X_n be an i.i.d. sample from a population with unknown mean μ and standard deviation σ. We take the sample mean = (X₁ + ··· + X_n)/n as an estimate for μ.

(a) According to Chebyshev's inequality, how large should the sample size n be so that with probability 0.99 the error | - μ| is less than 2 standard deviations?

(b) According to the central limit theorem, how large should n be so that with probability 0.99 the error | - μ| is less than 2 standard deviations?