7 The number of absences by girls from a certain class on any day is modelled by a random variable with distribution \(\operatorname { Po } ( 0.2 )\). The number of absences by boys from the same class on any day is modelled by an independent random variable with distribution \(\operatorname { Po } ( 0.3 )\).

1. Find the probability that, during a randomly chosen 2-day period, the total number of absences is less than 3 .
2. Find the probability that, during a randomly chosen 5-day period, the number of absences by boys is more than 3.
3. The teacher claims that, during the football season, there are more absences by boys than usual. In order to test this claim at the 5\% significance level, he notes the number of absences by boys during a randomly chosen 5-day period during the football season.
   (a) State what is meant by a Type I error in this context.
   (b) State appropriate null and alternative hypotheses and find the probability of a Type I error.
   (c) In fact there were 4 absences by boys during this period. Test the teacher's claim at the 5\% significance level.
   If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.