4 A fair spinner has five sides numbered \(1,2,3,4,5\). The score on one spin is denoted by \(X\).
- Show that \(\operatorname { Var } ( X ) = 2\).
Fiona has another spinner, also with five sides numbered \(1,2,3,4,5\). She suspects that it is biased so that the expected score is less than 3 . In order to test her suspicion, she plans to spin her spinner 40 times. If the mean score is less than 2.6 she will conclude that her spinner is biased in this way. - Find the probability of a Type I error.
- State what is meant by a Type II error in this context.