Answer:
0.9999
Step-by-step explanation:
Let X be the random variable that measures the time that a switch will survive.
If X has an exponential distribution with an average life β=44, then the probability that a switch will survive less than n years is given by
So, the probability that a switch fails in the first year is
Now we have 100 of these switches installed in different systems, and let Y be the random variable that measures the the probability that exactly k switches will fail in the first year.
Y can be modeled with a binomial distribution where the probability of “success” (failure of a switch) equals 0.0225 and
where
equals combinations of 100 taken k at a time.
The probability that at most 15 fail during the first year is