Standard +0.3 This is a straightforward confidence interval width calculation requiring the formula width = 2z*σ/√n, rearranging to find n, then rounding up. It's slightly above average difficulty because students must remember the width formula and correctly manipulate it, but it's a standard textbook exercise with no conceptual subtlety or multi-step reasoning.
2 Heights of a certain species of animal are known to be normally distributed with standard deviation 0.17 m . A conservationist wishes to obtain a \(99 \%\) confidence interval for the population mean, with total width less than 0.2 m . Find the smallest sample size required.
Attempt to arrange equ of correct form (with correct \(z\) and '\(2 \times\)' into the form \(n=\) or \(\sqrt{n} =\)
Smallest \(n\) is 20
A1 [4]
$z = 2.576$ | B1 | Seen (accept 2.574 to 2.579)
$2 \times z \times \frac{0.17}{\sqrt{n}} = 0.2$ o.e | M1 | Allow without '$2 \times$' OR with incorrect $z$
$n = \left(\frac{2 \times 0.17 \times 2.576}{0.2}\right)^2$ o.e (= 19.2) | M1 | Attempt to arrange equ of correct form (with correct $z$ and '$2 \times$' into the form $n=$ or $\sqrt{n} =$
Smallest $n$ is 20 | A1 [4] |
2 Heights of a certain species of animal are known to be normally distributed with standard deviation 0.17 m . A conservationist wishes to obtain a $99 \%$ confidence interval for the population mean, with total width less than 0.2 m . Find the smallest sample size required.
\hfill \mbox{\textit{CAIE S2 2013 Q2 [4]}}