A school-board administrator believes that the average number of days absent per year among students is less than 8 days. From past experience, she (the school-board administrator) knows that the population standard deviation is 3 days. In testing to determine whether her belief is true, she used a sample of 100 students and a 5% level ofsignificance.

Based on the above information, what is the probability of a Type II error, given that the true population average is 7.2 days? Show all the necessary steps to answer the question.