If Y has a x² distribution with n degrees of freedom then Y could be represented by ∑_{x = i}ⁿ x_i, where the x_i's are independent x² distributions, each with  degree of freedom.

a. Show that Z = (Y - n)/√2n has approximately a standard normal distribution for large values of n.

b. If y has a x² distribution with 30 degrees of freedom, find the approximate probability that Y falls within 2 standard deviations of its mean, i.e., find P(μ - 2σ < Y < μ + 2σ).