Moderate -0.3 Part (a) is a straightforward application of normal distribution tables and independence (find P(X<194) then cube it). Part (b) requires reading a diagram to estimate standard deviation using empirical rule properties, which is slightly less routine but still a standard technique. Overall slightly easier than average due to minimal problem-solving required.
The heights of English men aged 25 to 34 are normally distributed with mean 178 cm and standard deviation 8 cm .
Three English men aged 25 to 34 are chosen at random.
Find the probability that all three men have a height less than 194 cm .
The diagram shows the distribution of heights of Scottish women aged 25 to 34.
\includegraphics[max width=\textwidth, alt={}, center]{f2f45d6c-cfdc-455b-ab08-597b06a69f36-08_585_1477_909_342}
The distribution is approximately normal. Use the diagram in the Printed Answer Booklet to estimate the standard deviation of these heights, explaining your method.
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\begin{enumerate}[label=(\alph*)]
\item The heights of English men aged 25 to 34 are normally distributed with mean 178 cm and standard deviation 8 cm .\\
Three English men aged 25 to 34 are chosen at random.
Find the probability that all three men have a height less than 194 cm .
\item The diagram shows the distribution of heights of Scottish women aged 25 to 34.\\
\includegraphics[max width=\textwidth, alt={}, center]{f2f45d6c-cfdc-455b-ab08-597b06a69f36-08_585_1477_909_342}
The distribution is approximately normal. Use the diagram in the Printed Answer Booklet to estimate the standard deviation of these heights, explaining your method.
\end{enumerate}
\hfill \mbox{\textit{OCR H240/02 Q7 [6]}}