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Date May 2009 Marks available 2 Reference code 09M.2.sl.TZ1.4
Level SL only Paper 2 Time zone TZ1
Command term Find Question number 4 Adapted from N/A

Question

A random variable X is distributed normally with mean 450 and standard deviation 20.

Find \({\rm{P}}(X \le 475)\) .

[2]
a.

Given that \({\rm{P}}(X > a) = 0.27\) , find \(a\).

[4]
b.

Markscheme

evidence of attempt to find \({\rm{P}}(X \le 475)\)     (M1)

e.g. \({\rm{P}}(Z \le 1.25)\)

\({\rm{P}}(X \le 475) = 0.894\)     A1     N2

[2 marks]

 

a.

evidence of using the complement     (M1)

e.g. 0.73, \(1 - p\)

\(z = 0.6128\)     (A1)

setting up equation     (M1)

e.g. \(\frac{{a - 450}}{{20}} = 0.6128\)

\(a = 462\)     A1     N3

[4 marks] 

 

 

b.

Examiners report

It remains very clear that some centres still do not give appropriate attention to the normal distribution. This is a major cause for concern. Most candidates had been taught the topic but many had difficulty understanding the difference between \(z\), \(F(z)\), \(a\) and \(x\) . Very little working was shown which demonstrated understanding. Although the GDC was used extensively, candidates often worked with the wrong tail and did not write their answers correct to 3 significant figures.

a.

It remains very clear that some centres still do not give appropriate attention to the normal distribution. This is a major cause for concern. Most candidates had been taught the topic but many had difficulty understanding the difference between \(z\), \(F(z)\), \(a\) and \(x\) . Very little working was shown which demonstrated understanding. Although the GDC was used extensively, candidates often worked with the wrong tail and did not write their answers correct to 3 significant figures.

Many candidates had trouble with part (b), a majority never found the complement, instead using their GDCs to calculate the result, which many times was finding a for \(P(X \leqslant a) = 0.27\) instead of for \(P(X \geqslant a) = 0.27\) . Many others substituted the values of \(0.27\) or \(0.73\) into the equation, instead of the \(z\)-scores.

b.

Syllabus sections

Topic 5 - Statistics and probability » 5.9 » Normal distributions and curves.
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