Standardised limits of a shaded normal area, interval probabilities and the value exceeded by a given percentage

The times that adults take to solve a particular online puzzle are normally distributed with mean \(4.8\) minutes and standard deviation \(0.4\) minutes.

1. In the diagram below, which shows the curve of the standard normal distribution, the area shaded gives the probability that an adult chosen at random takes between \(4.3\) minutes and \(5.5\) minutes to solve the puzzle.[6]
   1. Write down the value of \(a\) and the value of \(b\).
   2. Calculate the probability that an adult chosen at random takes less than \(5.5\) minutes to solve the puzzle, and the probability that the adult takes between \(4.3\) minutes and \(5.5\) minutes.
2. \(6\%\) of adults take more than \(d\) minutes to solve the puzzle.[4]
   1. Draw a sketch similar to the diagram above, and shade clearly the area that represents this \(6\%\).
   2. Find the value of \(d\).