Question

A Denver Hospital reported having 3847 births in a recent yeat. This equates to an average rate of 10.5 babies born per day. Use the Poisson distribution to answer the questions.

a. What is the probability that in a day there are exactly 12 births?

b. What is the probability that more than 70 babies are born in a seven-day period?

Answer 1

solution:

average baby born per day = = 10.5

for mula for poisson distribution

a)

probability that there are exactly 12 births = P(X=12)

b)

average baby born per day = 10.5

average baby born in seven day = = 7*10.5 = 73.5

so X Poi (73.5)

since > 20, so we can use it as approximately normal distribution where X follows normal distribution with mean = and variance =

so X N ( 73.5, 73.5)

mean = 73.5

standard deviation =

we have to find the probability of more than 70 babies norn in seven day period = P(X > 70)

z score =

P(X > 70) = 1 - value of z to the left of -0.41 = 1 - 0.3409 = 0.6591