Standard +0.3 This is a standard inverse normal problem requiring students to set up two equations using z-scores from percentage points (10th and 20th percentiles), then solve simultaneously for μ and σ. While it involves multiple steps and careful algebraic manipulation, it's a routine application of normal distribution theory commonly found in A-level statistics with no novel insight required.
6.
Skilled operators make a particular component for an engine. The company believes that the time taken to make this component may be modelled by the normal distribution. They timed one of their operators, Sheila, over a long period.
They find that when she makes a component, she takes over 90 minutes to make one \(10 \%\) of the time, and that \(20 \%\) of the time, a component was less than 70 minutes to make.
Estimate the mean and standard deviation of the time Sheila takes to make a component.
6.
Skilled operators make a particular component for an engine. The company believes that the time taken to make this component may be modelled by the normal distribution. They timed one of their operators, Sheila, over a long period.
They find that when she makes a component, she takes over 90 minutes to make one $10 \%$ of the time, and that $20 \%$ of the time, a component was less than 70 minutes to make.
Estimate the mean and standard deviation of the time Sheila takes to make a component.\\
\hfill \mbox{\textit{SPS SPS SM Statistics 2026 Q6 [5]}}