The number of online customer service chats of a small company is believed to follow a Poisson distribution. Currently, these chats are handled by a single agent. The manager of the company knows from past experience that an additional agent will be needed if the rate of incoming online chats exceeds 10 per hour. During a randomly selected half-hour period, there were 7 chats observed. a) If the rate of online chats is actually 10 per hour, find the probability that 7 or more chats will come in during a given half-hour period. b) If the rate of online chats is actually 15 per hour, find the probability that 7 or more chats will come in during a given half-hour period. c) Would you advise the manager to hire a second operator? Justify your answer.

#NOTES: I JUST WANT c) ANSWER AND JUSTIFICATION BECAUSE I HAVE ASKED a AND b and the answers is 0.2378 for a and 0.622 for b. Thank you.