Confidence interval derived quantity

A question is this type if and only if it requires deducing a confidence interval for a derived quantity (such as circumference from diameter, or a linear transformation of the mean) directly from a confidence interval already calculated for the original variable.

1 questions · Standard +0.3

5.05d Confidence intervals: using normal distribution
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OCR S3 2009 June Q3
7 marks Standard +0.3
3 A machine produces circular metal discs whose radii have a normal distribution with mean \(\mu \mathrm { cm }\). A random sample of five discs is selected and their radii, in cm, are as follows. $$\begin{array} { l l l l l } 6.47 & 6.52 & 6.46 & 6.47 & 6.51 \end{array}$$
  1. Calculate a \(95 \%\) confidence interval for \(\mu\).
  2. Hence state a 95\% confidence interval for the mean circumference of a disc.