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June 2019 p63 q1
3201
The time taken, in minutes, by a ferry to cross a lake has a normal distribution with mean 85 and standard deviation 6.8.
Over a long period it is found that 96% of ferry crossings take longer than a certain time \(t\) minutes. Find the value of \(t\).
Solution
Given that 96% of ferry crossings take longer than \(t\), this implies that 4% take less time than \(t\). We need to find the corresponding \(z\)-value for the 4th percentile of the standard normal distribution.
The \(z\)-value for 4% in the standard normal distribution is approximately \(z = -1.751\).