| Date | None Specimen | Marks available | 4 | Reference code | SPNone.2.sl.TZ0.5 |
| Level | SL only | Paper | 2 | Time zone | TZ0 |
| Command term | Find and Write down | Question number | 5 | Adapted from | N/A |
Question
The probability of obtaining heads on a biased coin is 0.4. The coin is tossed 600 times.
(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.
Markscheme
(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]
