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Date May 2008 Marks available 3 Reference code 08M.2.sl.TZ1.6
Level SL only Paper 2 Time zone TZ1
Command term Find Question number 6 Adapted from N/A

Question

A factory makes switches. The probability that a switch is defective is 0.04. The factory tests a random sample of 100 switches.

Find the mean number of defective switches in the sample.

[2]
a.

Find the probability that there are exactly six defective switches in the sample.

[2]
b.

Find the probability that there is at least one defective switch in the sample.

[3]
c.

Markscheme

evidence of binomial distribution (may be seen in parts (b) or (c))     (M1)

e.g. np, \(100 \times 0.04\)

\({\text{mean}} = 4\)     A1     N2

[2 marks]

a.

\({\rm{P}}(X = 6) = \left( {\begin{array}{*{20}{c}}
{100}\\
6
\end{array}} \right){(0.04)^6}{(0.96)^{94}}\)     (A1)

\( = 0.105\)     A1     N2

[2 marks]

b.

for evidence of appropriate approach     (M1)

e.g. complement, \(1 - {\rm{P}}(X = 0)\)

\({\rm{P}}(X = 0) = {(0.96)^{100}} = 0.01687 \ldots \)     (A1)

\({\rm{P}}(X \ge 1) = 0.983\)     A1     N2

[3 marks]

c.

Examiners report

Part (a) was handled well by most students.

a.

Although this question was a rather straightforward question on binomial distribution, parts (b) and(c) seemed to cause much difficulty.

b.

Although this question was a rather straightforward question on binomial distribution, parts (b) and(c) seemed to cause much difficulty. In part (c), finding at least one defective switch, many forgot to take the complement.

c.

Syllabus sections

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