Question

Surgery is in 4 out if every 10 hospital emergency room visits. If a large urban hospital had 840 emergency visits in the past month how many of these visits would you expect to required surgery

Answer 1

Answer:

Expected number of visits to the emergency room that would require a surgery is 336.

Step-by-step explanation:

Let X = number of surgery.

The odds of having a surgery in a randomly selected visit to a emergency room is 4 out of 10.

Then the probability of having a surgery in a randomly selected visit to a emergency room is:

$p=\frac{4}{10}=0.40$

In the past month a large urban hospital had 840 emergency visits.

An emergency room visit may lead to surgery or not is independent of the others.

The random variable X follows a Binomial distribution with parameters n = 840 and p = 0.40.

The expected value of a binomial random variable is:

$E(X)=np$

Compute the expected number of visits that would require a surgery as follows:

$E(X)=np$

         $=840\times 0.40\\=336$

Thus, expected number of visits to the emergency room that would require a surgery is 336.