(i)     Write down the mean number of heads.

(ii)    Find the standard deviation of the number of heads.

Find the probability that the number of heads obtained is less than one standard deviation away from the mean.

(i) recognizing binomial with \(n = 600\) , \(p = 0.4\)     M1

\({\rm{E}}(X) = 240\)     A1     N2

(ii) correct substitution into formula for variance or standard deviation     A1

e.g. 144, \(\sqrt {600 \times 0.4 \times 0.6} \)

sd = 12     A1     N1

[4 marks]

attempt to find range of values     M1

e.g. \(240 \pm 12\) \(228 < X < 252\)

evidence of correct approach     A1

e.g. \({\rm{P}}(X \le 251) - {\rm{P}}(X \le 228)\)

\({\rm{P}}(228 < X < 252) = 0.662\)     A1     N2

[3 marks]