Moderate -0.8 This is a straightforward application of the sampling distribution of the mean formula (σ/√n) followed by a single normal probability calculation. It requires only direct recall of standard results with no problem-solving or conceptual challenges beyond recognizing the setup.
1 The number of words on a page of a book can be modelled by a normal distribution with mean 403 and standard deviation 26.8. Find the probability that the average number of words per page in a random sample of 6 pages is less than 410.
For standardising a normal distribution with mean 403; For correct denom (can be implied); For using tables and finding correct area ie > 0.5
$P(X < 410) = \Phi\left(\frac{410-403}{26.8/\sqrt{6}}\right) = \Phi(0.6398) = 0.739$ | M1, A1, M1, A1 (4 marks) | For standardising a normal distribution with mean 403; For correct denom (can be implied); For using tables and finding correct area ie > 0.5
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1 The number of words on a page of a book can be modelled by a normal distribution with mean 403 and standard deviation 26.8. Find the probability that the average number of words per page in a random sample of 6 pages is less than 410.
\hfill \mbox{\textit{CAIE S2 2005 Q1 [4]}}