The Chen, Wang, and Li law firm produces many legal documents that must be word processed for clients and the firm. Requests average eight pages of documents per hour, and they arrive according to a Poisson distribution. The secretary can word process $10$ pages per hour on average according to an exponential distribution.

$($a$)$ What is the average utilization rate of the secretary$?$

$($b$)$ What is the probability that more than four pages are waiting or being word $(5)$ processed?