The number of people entering the intensive care unit at a

Solution :

Step 1 of 2:

Given the poisson distribution with a mean equal to five person.

Here =5.

Our goal is:

a). We need to find to find the probability that the number of people entering the intensive

     care unit on a particular is equal to 2.

b). We need to find is it likely that Y will exceed 10.Explain.

a).

Now we have to find the probability that the number of people entering the intensive care unit on a particular is equal to 2.

The formula of the poisson probability is

P(X=k)=

Where k is the actual number of successes that result from the experiment.

e is approximately equal to 2.71828.

Let k=2.

P(X=2)=

P(X=2)=

P(X=2)=

P(X=2)= 0.0842

Then the probability of less than or equal to 2 is

P(X2)=P(X=0)+P(X=1)+P(X=2)

Where, P(X=0)+P(X=1)+P(X=2) is obtained from Excel by using the function

“=poisson(x,,false)”

We know that =5.

Then the table is given below.

Now,

P(X2)= P(X=0)+P(X=1)+P(X=2)

P(X2)= 0.006738+0.03369+0.084224

P(X2)= 0.124652

Therefore the probability of less than or equal to 2 is 0.124652.