Question

1. Answer the following.

1. (3) Babies are born at a rate of 2 per hour at the local hospital. What is the probability that none would be born in a two hour period?
2. (3) What is the probability that the time before the next birth is in less than one hour?
3. (3) In a total of 10 births what is the probability that 6 will be boys if the probability of a boy is 0.51?

Answer 1

a) Average number of babies born in 1 hour = 2

Therefore in 2 hour period, the number of average babies born = 2*2 = 4

Probability that none would be born in 2 hour period is computed using poisson probability function as:

= e^-4 = 0.0183

Therefore 0.0183 is the required probability here.

b) Average waiting time for a baby to born = 1/2 hour

Probability that the time before the next birth is in less than one hour is computed as:

Therefore 0.8647 is the required probability here.

c) P(boy ) = 0.51

Therefore number of boys out of 10 born is modelled here as:

Therefore 0.2130 is the required probability here.