1. Consider Caleb the basketball player. In a game, he shoots 10 free throws. In the year, he makes 70% of his free throws. Is this a binomial setting? Fully explain your response.

2. Assuming that Caleb makes 70% of his free throws and shoots 10 free throws in a game, what is the probability that he will make a) all 10 of his free throws in a game? b) seven or more of his free throws in a game?

c) Find the mean number of free throws Caleb would make in the game.

3. Describe the four conditions of a binomial setting.

4. Consider testing a batch of 20 lightbulbs from a certain unnamed company. Let X be the number of properly functioning lightbulbs. a) What is the standard deviation of X if the lightbulbs function properly 80% of the time? b) What is the standard deviation of X if the lightbulbs function properly 90% of the time? c) What is the standard deviation of X if the lightbulbs function properly 95% of the time? d) What is the standard deviation of X if the lightbulbs function properly 99% of the time? e) What does your work show about the behavior of the standard deviation of a binomial distribution as the probability of success approaches one?

5. The random walk theory of stocks in the stock market assumes there is a 0.67 chance that an index of stocks will increase in value in any given year. Furthermore, the index in any given year is not influenced by its previous year's performance. Let X be the number of years in which the index increased among the next 10 years' time. a) Verify that this can be modeled by a binomial distribution and write the notation. b) What are the possible values of X? c) Construct a probability distribution table. d) What are the mean and standard deviation of X?