Standardised limits of a normal interval of battery lifetimes on a standard normal curve, two probabilities and the time exceeded by a given percentage

The time for which a fully charged battery of a certain type powers a torch is normally distributed with mean \(18.5\) hours and standard deviation \(1.6\) hours.

1. The probability that such a battery lasts between \(17.7\) hours and \(20.9\) hours is shown by the shaded area on the standard normal curve below.[5]
   1. Write down the value of \(a\) and the value of \(b\).
   2. Find the probability that a battery lasts more than \(17.7\) hours, and the probability that it lasts between \(17.7\) hours and \(20.9\) hours.
2. \(85\%\) of these batteries last longer than \(t\) hours.[5]
   1. Sketch a standard normal curve, like the one in part (a), and shade clearly the area that represents the \(85\%\).
   2. Find the value of \(t\).