In part (i) you are asked a question about the distribution of the times that the candidates took. So to answer this, assuming that the times are normally distributed, you need to use the mean and the standard deviation of the distribution of those times.
On the other hand, in part (ii), you are asked a question about the distribution of the
mean of the times taken rather than the distribution of the times taken. This is the reason underlying dividing by n here.
To understand a little more about the distribution of the mean, think about doing this experiment a large number of times - so repeated samples of 50 candidates each given the test and each time you calculate the mean time taken to complete. These mean times will have a distribution, and it is this that we are concerned with here.
It turns out that if the original
population of times is normal (imagine every student there is and every time that they would take if they sat the test) with mean
μ and variance
σ2, then the distribution of means of repeated samples of size
n will be normal with mean
μ and variance
nσ2.