In one of the archaeological excavation sites the artifact d

In one of the archaeological excavation sites, the artifact density (number of prehistoric artifacts per 10 liters of sediment) was 1.0 Suppose you are giong to dig up and examine 70 liters of sediment at this site. Let r = 0,1,2,3,... be a random variable that represents the number of prehistoric artifacts found in your 70 liters of sediment. Compute the probability that in your 70 liters of sediment that you will find 3 prehistoric artifacts. Round your answer to the nearest ten thousandth.

Solution

There is an average of 1.0 artifacts per 10 L, so there\'s an average of 7.0 artifacts per 70 L.

Note that the probability of x successes out of n trials is          
          
P(x) = u^x e^(-u) / x!          
          
where          
          
u = the mean number of successes =    7      
          
x = the number of successes =    3      
          
Thus, the probability is          
          
P (    3   ) =    0.052129252 = 0.0521 [ANSWER]