Final answer:
The probability distribution of X, the number of Canadian men who will develop prostate cancer out of a random sample of 180, can be represented by a binomial distribution.
Step-by-step explanation:
The probability distribution of X, the number of Canadian men out of a random sample of 180 who will develop prostate cancer, can be represented by a binomial distribution.
The probability of success, p, is 1/9 because it is estimated that 1 in 9 Canadian men will develop prostate cancer during their lifetime. The number of trials, n, is 180, which represents the sample size.
To calculate the probability distribution, we can use the binomial probability formula: P(X=k) = C(n,k) * p^k * (1-p)^(n-k), where C(n,k) is the number of combinations of n items taken k at a time.
We can calculate the probability of each possible outcome (from 0 to 180) using this formula.