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. (Note your calculations may be given in scientific notation by your calculator.)Compute the mean, ??, and the standard deviation, ??, for the random variable X. (We are still using the case of 2 cases of testicular cancer. Do not attempt this for the population of 2500.) 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.