a.A sensor network consists of a large number of microprocessors spread out over an area, in communication with each other and with the base station. In a certain network, the probability that the message will fail to reach the base station is 0.005. Assume that during a particular day, 1000 messages are sent.

i.What is the probability that exactly 3 of the messages fail to reach the base station

3 marks

ii.What is the probability that fewer than 994 of the messages reach the base station

4 marks

iii.What is the mean of the number of messages that fail to reach the base station

1 mark

What is the standard deviation of the number of messages that fail to reach the base station