1. Let the random variable X be the number of successes in n=30 independent Bernoulli trials with probability p=0.6
of success on each trial. Find the probability of getting at most 25 successes in the n=30 independent trials.
a. (3 pts) Use the binomial distribution.
b. (3 pts) Use the normal approximation without the continuity correction.
c. (3 pts) Use the normal approximation with the continuity correction.
2. Suppose that Kenyon College would like to have an entering class of 415 students next year (this was actually the target for the class of 1998). Past experience shows that about 27% of the students admitted will accept Kenyon's offer. Answer the following questions assuming that the college decides to admit 1400 students and the students make their decisions independently.
a. (2 pts) What is the distribution of the number of students who accept?
b. (4 pts) What are the mean and variance of the number of students who accept?
c. (3 pts) What is the probability that the college gets more students than they want?
d. (6 pts) The college actually admitted 1535 students. Redo part c using this information.
Section 5.1 - 5.8, 5.10, 5.18, 5.22
Section 5.2 - 5.24, 5.26, 5.30, 5.32, 5.37, 5.40