5 The lengths of videos of a certain popular song have a normal distribution with mean 3.9 minutes. \(18 \%\) of these videos last for longer than 4.2 minutes.
- Find the standard deviation of the lengths of these videos.
- Find the probability that the length of a randomly chosen video differs from the mean by less than half a minute.
The lengths of videos of another popular song have a normal distribution with the same mean of 3.9 minutes but the standard deviation is twice the standard deviation in part (i). The probability that the length of a randomly chosen video of this song differs from the mean by less than half a minute is denoted by \(p\). - Without any further calculation, determine whether \(p\) is more than, equal to, or less than your answer to part (ii). You must explain your reasoning.