Probability

Question

According to a recent article the average number of babies born with significant hearing loss (deafness) is approximately four per 1,000 babies in a healthy baby nursery. The number climbs to an average of 30 per 1,000 babies in an intensive care nursery.

Suppose that 1,000 babies from healthy baby nurseries were randomly surveyed. Find the probability that exactly four babies were born deaf. (Round your answer to four decimal places.)

I'm not exactly sure how to get the answer, I've tried dividing 30 by 1000 then multiply it by 4 but it's not the answer

Answer 1

One way to think of this problem is to imagine that you were taking lots of 1,000 baby samples. In some samples you would find no hearing loss babies. In some samples you would find 1 hearing loss baby in the group of 1,000. In other samples you would find 2, 3, 4, 5, 6, 7, 8 and so on. On the average, they find 4 babies with hearing loss per sample.

 

So, the question is, out of all those samples out there, what is the probability that your sample has exactly 4 babies with hearing loss? 

 

This is actually given by the binomial distribution. If we think of the average as a rate, that is the probability of selecting a deaf baby is .004, then we want

 

(1000 take 4) times .004 to the 4th power times .996 to the 996th power. This works out to be about .2, or the probability of getting a sample with exactly 4 deaf babies is 20%. so, let me know if this is the right answer.