Psychology Problems Advice Info

(1) If I give you a coin to flip and I tell you it is not a fair coin, but is weighted to come up heads on average only 20% of the time (instead of 50%), what is the most likely number of heads you would observe in a series of 15 flips? If the coin was truly weighted to come up heads on average only 20% of the time, what is the probability that you would observe 9 or more heads in a series of 15 flips? What is the probability that you would observe 2 or fewer heads in a series of 15 flips?

(2) (12 pts) a student is taking a multiple-choice exam with 16 questions. Each question has five alternatives. If the student guesses on 12 of the questions, what is the probability she will guess at least 8 correct? Assume all of the alternatives are equally likely for each question on which the student guesses.

(3) Use Table B to answer the following questions:

a. In the binomial distribution, as N decreases, what happens to the value of the most likely outcome?

b. For any N, as the probability of an event (P or Q) increases from .05 to .50, what happens to the value of the most likely outcome (i.e., “number of P or Q events”)?

c. For P or Q = .5, what happens to the probabilities of the very most extreme outcomes (the highest and lowest “number of P or Q events” as N increases?

d. If you were to create a histogram of binomial probabilities, what happens to the shape of the distribution as N increases (compared to the normal distribution)?