Question: A sensor network consists of a large number of microprocessors spread out over an area, in communication with each other and with a base station.

A sensor network consists of a large number of microprocessors spread out over an area, in communication with each other and with a base station. In a certain network, the probability that a message will fail to reach the base station is 0.005. Assume that during a particular day, 1000 messages are sent.
a. What is the probability that exactly 3 of the messages fail to reach the base station?
b. What is the probability that fewer than 994 of the messages reach the base station?
c. What is the mean of the number of messages that fail to reach the base station?
d. What is the standard deviation of the number of messages that fail to reach the base station?

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