Suppose the COVID vaccination rate is 68% in your area. This rate is determined by taking the ratio of fully vaccinated people - those who received the full dose of vaccine, either with or without a booster - to the total number of people. 25 people are randomly selected from your area and their vaccination status is checked to determine how many are fully vaccinated.

A)

1. Determine the following
2. What is the random variable? Is it continuous or discrete?

1. What is the mean number of people who are fully vaccinated?

1. What are the variance and standard deviation?

B). Calculate the probability that exactly68% of the sample will be vaccinated. Use the binomial formula and show your work!Report your answer to 4 decimal places.

C)

1. What is the probability that no more than two people will be not fully vaccinated? (This means 0, 1, or 2 people not vaccinated; consider what this means about the number of people who ARE fully vaccinated). Use the method of your choice for your calculations, and report to 4 decimal places. Would this be considered unusual?