Please help me with this question!

used formulas.) Historic data suggests that a library book will be returned in one week with probability 0.60. Otherwise, it is considered late, and fees begin to be charged. A librarian is interested in monitoring a random sample of 10 books. a) (2) Let X= number of books among 10 that are returned within one week. Describe the distribution of X and explain how the experiment satises the underlying assumptions associated with the stated distribution. b) (2) What is the probability that between four and six books (inclusive) Will be returned in one week? c) (2) What is the probability that at least 7 books will be returned in one week? (1) (2) Among the 10 books sampled, what is the expected number that will be returned late? e) (4) Recently several public libraries around Canada have removed late fees. One month after the library adopts this policy the librarian is interested in investigating Whether it has had a positive effect on the proportion of books returned in one week. The librarian randomly samples 40 books and monitors them. Of these 40 books 27 are retumed in one week. At a 5% level of signicance, does the data suggest that the proportion of books returned in one week has increased? Perform a hypothesis test outlining all four steps and making a clear conclusion (The critical value should be used to make your conclusion)