Question

As a hospital administrator responsible for staffing, I need to schedule the appropriate hospital staff members in key areas in order to provide proper care. In a recent​ year, my hospital had 4,320 births. Find the mean number of births per​ day, then use that result and the Poisson distribution to find the probability that in a​ day, there are 13 births. Does it appear likely that on any given​ day, there will be exactly 13 ​births? If it is likely than I will need to adjust my staffing personnel to cover the staff.

If I select incorrectly, I may risk not being able to provide proper care to patients in need where it can be life-threatening and the hospital and myself will be held accountable.

The mean number of births per day is _______________. ​(Round to one decimal place as​ needed.)

The probability​ that, in a​ day, there are 13 births is ___________________. ​(Round to three decimal places as​ needed.)

With your calculated answers, briefly describe the probability of having 13 births in one day.

Answer 1

The mean number of births per day = 4320 / 365 = 11.84

Using Poisson distribution with mean 11.84,

Probability of 13 births in a day, P(13, 11.84) = = 0.104

exp-13 + x11.84 13!

The probability of having 13 births in one day is 0.104. So it is possible to have 13 births in one day, but the probability is quite low.