BlueLagoon is a new eco resort where visitors can either stay in villas or suites. 70% of the guests prefer to stay in a villa, while the rest prefer to stay in a suite. On a particular day, there were 15 visitors waiting to get checked-in to the resort.

a) What is the mean value and the standard deviation of the number of people who prefer to stay in a villa?

b) What is the probability that the number of people who want a villa is more than two standard deviations away from the mean value?

c) BlueLagoon only has 13 villas and 10 suites available at the resort. If the 15 people get checked-in one after another, what is the probability that all of them will be able to stay at their preferred type of accommodation?