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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.

[4]
a(i) and (ii).

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

[3]
b.

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]

a(i) and (ii).

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]

b.

Examiners report

[N/A]
a(i) and (ii).
[N/A]
b.

Syllabus sections

Topic 5 - Statistics and probability » 5.8 » Binomial distribution.
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