CAIE S1 2017 June — Question 5

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2017
SessionJune
TopicNormal Distribution
TypeFind standard deviation from probability

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.
  1. Find the standard deviation of the lengths of these videos.
  2. 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 \(p\).
  3. 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.