The time, \(X\) hours, for which students use a games machine in any given day has a normal distribution with mean 3.24 hours and standard deviation 0.96 hours.
On how many days of the year ( 365 days) would you expect a randomly chosen student to use a games machine for less than 4 hours?
Find the value of \(k\) such that \(\mathrm { P } ( X > k ) = 0.2\).
Find the probability that the number of hours for which a randomly chosen student uses a games machine in a day is within 1.5 standard deviations of the mean.
The variable \(Y\) is normally distributed with mean \(\mu\) and standard deviation \(\sigma\), where \(4 \sigma = 3 \mu\) and \(\mu \neq 0\). Find the probability that a randomly chosen value of \(Y\) is positive.
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