T/F Test - Chris Again! Chris is sitting a true-false statistics test, which con

Question

T/F Test - Chris Again! Chris is sitting a true-false statistics test, which consists of 13 items. After the test, Chris told you he didn’t study for the test at all and guessed all answers. (a) If Chris guessed each and every item in the test, describe the probability distribution for the number of correct guesses. Present the probability distribution in the form of a table using 6 decimal points in your answers. (Use Excel to calculate the probabilities.) (b) Using the formula: E(X) = XP(X), find out the number of correct answers Chris would expect to get. (You can use Excel to do the calculation. Just copy the Excel output onto your Word document.) (c) What does expectation mean in statistics? Explain your answer in the context of the T/F Test. (d) What is the probability that Chris gets 11 or more correct answers for this test? (e) When the result was released, Chris got 11 out of 13. Would you be surprised? Do you think Chris lied to you? Explain your answer.

Explanation / Answer

c.

This means that Chris will get 6.5 correct answers on an average.

d.

P(X>=11) = P(X = 11) + P(X = 12) + P(X = 13) = 0.104736 + 0.019043 + 0.001587 = 0.125366

e.

Yes I would be surprised as the probability of getting 11 answers correct is 0.104736 which is quite low. Yes, Chris may have lied.

a. Binomial Distribution n= 13 p= 0.5 Mean=np= 6.5 Variance=np(1-p)= 3.25 Standard Deviation= 1.802776 Probability Distribution x P(X=x) x*P(X=x) 0 0.000122 0.000000 1 0.001587 0.001587 2 0.009521 0.019043 3 0.034912 0.104736 4 0.08728 0.349121 5 0.157104 0.785522 6 0.209473 1.256836 7 0.209473 1.466309 8 0.157104 1.256836 9 0.08728 0.785522 10 0.034912 0.349121 11 0.009521 0.104736 12 0.001587 0.019043 13 0.000122 0.001587 b. E(X)= 6.500000

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.