Question

The table contains a hospital's probability distribution chart of the number of babies born per day for a week. Determine the missing probability inthe distribution, and then answer this question: What percentage of time should a sufficient number of nurses be on duty to care for at least sevenbabies? (Answer to the nearest tenth of a percent.)babies/daY

Answer 1

Recall that the sum of all probabilities should up to 1. Let x be the probability of 11-14 babies/day.

Then we have the equation

$0.125+0.25+0.4375\text{ + x + 0 = 1}$

which is equivalent to the equation

$x+0.8125\text{ = 1}$

So by subtracting 0.8125 on both sides we get

$x\text{ = 1-0.8125 = 0.1875}$

So the probability of having 11-14 babies/day is 0.1875.

Now, to calculate the probability having at least 7 babies, we simply add the probabilities of the events where we have more than 7 babies. That is, sum 7-10 and 11-14 probabilities, which is

$0.4375+0.1875\text{ = 0.625}$

which is close to 63% of the time