(3 pts) A multiple choice exam consists of 10 questions. Assume each question ha
ID: 3064826 • Letter: #
Question
(3 pts) A multiple choice exam consists of 10 questions. Assume each question has five possible answers, of which only one is correct a.) If a student selects one answer at random (guesses) for a particular question, what is the probability that 5. it is the correct answer? 5 b.) What is the probability that the student will get between 2 and 3 questions correct inclusive? C) what is the probability that the student will get at least a B (80% or better) on the exam? The student would have to guess at least 8 questions correctly d.) How many questions out of the ten would you expect the student to guess correctly on average? e.) What is the standard deviation of the number of questions that the student would guess correctl (1.5 pts) Which of the following are binomi experiment, state why a.) Four cards are select one at a time without replacement from a standard deck of 52 cards. 6. al experiments? If a scenario does not describe a binomial Let x represent the number of aces among the four cards. 4 3 2 52 5 50 4 b.) A die is rolled 20 times and the number of fives that occurred is recorded. c.) A couple plans to keep having children until they get at least one child of each sex up to a maximum of 6 kids. 2 possilbke oot comes of trvalsis nt FixedExplanation / Answer
5) p = 1/5 = 0.2
n = 10
a) P(X = 1) = 10C1 * (0.2)^1 * (0.8)^9 = 0.2684
b P(2 < X < 3) = P(X = 2) + P(X = 3)
= 10C2 * (0.2)^2 * (0.8)^8 + 10C3 * (0.2)^3 * (0.8)^7 = 0.5033
c) P(X > 8) = P(X = 8) + P(X = 9) + P( = 10)
= 10C8 * (0.2)^8 * (0.8)^2 + 10C9 * (0.2)^9 * (0.8)^1 + 10C10 * (0.2)^10 * (0.8)^0 = 0.0008
d) Expected no of correctly guessed question = n * p = 10 * 0.2 = 2
e) Standard deviation = sqrt(n * p * (1 - p))
= sqrt(10 * 0.2 * 0.8)
= 1.2649
6) Only a and b
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.