(a(i))[4]
Zak goes for a run once each week. The length of time he takes, measured in minutes, follows a normal distribution with mean $35.2$ and standard deviation $4.7$. Determine the expected number of days in a year ($52$ weeks) when Zak’s run takes less than $30$ minutes.
(a(ii))[3]
The probability that Zak’s time lies between $35.2$ minutes and $t$ minutes, where $t > 35.2$, is $0.148$. Determine the value of $t$.
(b)[5]
The random variable $X$ follows the distribution $N(\mu, \sigma^2)$. It is known that $P(X < 7) = 0.2119$ and $P(X < 10) = 0.6700$. Determine the values of $\mu$ and $\sigma$.