During the morning hours at a catalog sales department, telephone calls come in at the rate $($Poisson$)$ of $30$ per hour. Calls that cannot be answered immediately are put on hold. The system can handle $6$ callers on hold. If additional calls come in$,$ they receive a busy signal. The $3$ customer service representatives who answer the calls spend an average of $2\mathrm{.}4$ minutes with a customer. Use Table $18\mathrm{.}4.$

a$.$ What is the probability that a caller will get a busy signal? $($Hint$.$ Solve for log $K$ or In $K$ using trial and error.$)($Do not round intermediate calculations. Round your answer to $5$ decimal places.$)$

Probability

b$.$ What is the probability that a customer will be put on hold? $($Do not round intermediate calculations. Round your answer to $3$ decimal places.$)$

Probability