Recall that the binomial distribution is given by b(x; n, ) = n x x (1 ) nx which has mean n and variance n(1 ).

(i) If X has distribution b(x; 10, 0.4) find P(X = 5).

(ii) Use the normal distribution to approximate P(X = 5).

(iii) Use the normal distribution to approximate the probability that X lies within 2 standard deviations of the mean.

(iv) What does Chebyshev's Theorem tell us about the probability that X lies within 2 standard deviations of the mean?