Question:
A quiz contains 8 multiple choice questions, each with 4 choices.
a. If you guess completely at random on one question, what is your probability p of getting the question right?
b. For the quiz, you randomly guess on each question independently. Consider the number X of exercises that you may get right. State parameters n and p for this binomial experiment (be sure to label each).
c. Say briefly why each of the 4 conditions are reasonably satisfied for this to be a Binomial experiment.
For the following parts, calculate the binomial probabilities. You may use any method (table, Excel, by hand, or calculator) unless specified – if you use a calculator or Excel, please write the command(s) that you used to get to your answer, show work otherwise. If the statement is in words, be sure to put it in symbols before calculating.
d. P(X = 6)
e. The probability that you get at least 7 of the questions correct. Calculate by hand and using the table.
f. P(X {eq}leq {/eq} 4) Use the table and Excel.
g. The probability that you get fewer than 3 questions correct.
h. Calculate the mean and variance of the number of questions that students get correct on an 8 problem quiz by just guessing.
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