Scenario: a worn out bottling machine does not properly apply caps to 5% of the bottles it fills. use scenario: if you randomly select 20 bottles from those produced by this machine, what is the approximate probability that exactly 2 caps have been improperly applied?

P = 0.356

Step-by-step explanation:

The machine has a 5% probability of not properly appliying the cap to a bottle.

This, in decimal form is p1 = 0.05

Then the probability of appliyinc correctly the cap is equal to p2 = 0.95

If we select 20 bottles and only two of them have problem with the cap, the probability will be:

P = 0.05^2*0.95^18

Because we have two bottles that landed in the 0.05 and 18 bottles that landed in the 0.95

P = 0.0089

But we have 20 oppotunties to land with those porbabilities for each botle, so the probability is:

Pt = 2*20*0.089 = 0.356