Assume that when adult males are randomly selected, 21% do not require vision correction (based on data from a Vision Council survey). Suppose 8 adult males are randomly selected. Answer the following:

1. What is the probability that exactly two adult males in the sample do not require vision correction? Provide both the R command used and the answer
2. What is the probability that half or fewer of the sample of adult males do not require vision correction? Provide both the R command used and the answer.
3. What is the probability that more than 75% of the sample of adult males do not require vision correction? Provide both the R command used and the answer.
4. Find the expected number of adult males in the sample who do not require vision correction.
5. What is the probability that half or fewer of the sample of adult males do not require vision correction? Provide both the R command used and the answer.