Probability using binomial distribution.

1. 30 percent of the population in a south-western community are Spanish speaking Americans. A Spanish speaking person is accused of killing a non Spanish speaking American and goes to trial.  Of the first 12 potential jurors only 2 are Spanish speaking Americans, and 10 are not.  The defendant's lawyer challenges the jury selection claiming bias against her client.  The government lawyer disagrees saying that the probability of this particular jury composition is common.  Compute the probability and discuss the assumptions

2. Dr Richmond, a psychologist is studying the daytime television viewing habits of college students.  She believes 45 percent of college students watch soap operas during the afternoon.  To further investigate, she selects a sample of ten.

Develop a probability distribution for the number of students in the sample who watch soap operas.

a. Find out the mean and standard deviation of this distribution.

b. What is the probability of finding exactly four watch soap operas?

c. What is the probability less than half of the students selected watch soap operas?