SOLUTION: at a hospital maternity ward, the hospital staff wants a probability distribution for the number of babies arriving each hour. what is the probability exactly 7 babies are born

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Question 460443: at a hospital maternity ward,
the hospital staff wants a probability distribution for the number of babies arriving each hour.
what is the probability exactly 7 babies are born during the next hour?
what is the probability than fewer than 3 babies are born during the next hour?
Answer by Tatiana_Stebko(1539) About Me  (Show Source):
You can put this solution on YOUR website!
If the expected number of occurrences in this interval is a, then theprobability that there are exactly k occurrences is equal to
P%28k%2Ca+%29=%28%28a%5Ek%29e%5E%28-a%29%29%2Fk%21, where
e is the base of the natural logarithm (e = 2.71828...)
k is the number of occurrences of an event — the probability of which is given by the function
k! is the factorial of k
a is a positive real number, equal to the expected number of occurrences during the given interval.
Babies arrive at an average of 8 babies per hour, so a=8
1) what is the probability exactly 7 babies are born during the next hour?
k=7
P%287%2C8+%29=%28%288%5E7%29e%5E%28-8%29%29%2F7%21=0.1396
2) what is the probability that fewer than 3 babies are born during the next hour?
Fewer than 3 - means that 0 babies (k=0) or 1 baby (k=1) or 2 babies (k=2) are born during the next hour
P%28fewer+than+3%29=P%280%2C8%29%2BP%281%2C8%29%2BP%282%2C8%29