Question

For ease of calculations, we will assume a binomial distribution with proportion of men having testicular cancer being 1 in 250, or ? = 0.004. We will assume half of the population of Prairie Grove is male and not worry about age of diagnosis being a factor. So, ? = 2500. State the probability distribution for the number of males who have testicular cancer. Be sure to show that the two properties required for a probability distribution are satisfied. Before we continue to create the statistical argument to answer our question of whether there appears to be a cancer cluster, we will take some time working with only two men.

Answer 1

Let X : Number of males having testicular cancer

X ~ Binomial ( n, p )

Here n = 2500 (Half the population of Prairie Grove)

and p = 1/250 = 0.004

Thus

X ~ Binomial ( 2500, 0.004 )

The two properties for binomial distribution are :

1. The number of trials should be fixed. Here n = half population of Prairie Grove is fixed at the time of setting up the model.

2. There are only two outcomes : success or failure.

Success is the person having testicular cancer while failure is person not having testicular cancer.

Only two outcomes, forming an collectively exhaustive and mutually exclusive sample space.