Once a week Zak goes for a run. The time he takes, in minutes, has a normal distribution with mean 35.2 and standard deviation 4.7.
Find the expected number of days during a year ( 52 weeks) for which Zak takes less than 30 minutes for his run.
The probability that Zak's time is between 35.2 minutes and \(t\) minutes, where \(t > 35.2\), is 0.148 . Find the value of \(t\).
The random variable \(X\) has the distribution \(\mathrm { N } \left( \mu , \sigma ^ { 2 } \right)\). It is given that \(\mathrm { P } ( X < 7 ) = 0.2119\) and \(\mathrm { P } ( X < 10 ) = 0.6700\). Find the values of \(\mu\) and \(\sigma\).