SPS SPS SM Statistics 2026 January — Question 6

Exam BoardSPS
ModuleSPS SM Statistics (SPS SM Statistics)
Year2026
SessionJanuary
TopicNormal Distribution
TypeEstimate from percentile/frequency data

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.