3. (25 points) A stulent is given aui exam with 10 oultiple choice questions. Fo

Question

3. (25 points) A stulent is given aui exam with 10 oultiple choice questions. For each question, the student is to select the best answer from aniong 4 multiple choices. Let X denote the nutaber of ques tions answered correctly on the exam by the student. the name for the probability distribution of the randon variable X i. Chi-Squared ii. Normal Binomial v. Gaussian (b) Select the probability mass function for the random variable X by circling the letter (A, B, C) above the table and compute the cumulative probabilities. 0 0.0317 1 0.1267 2 0.2323 3 0.2581 4 0.1936 5 0.1032 6 0.0401 7 0.0115 8 0.0024 9 0.0004 1 0.1267 2 0.2323 3 0.2581 0.1936 5 0.1032 6 0.0401 7 0.0115 8 0.0024 9 0.0004 0 0.0563 1 0.1877 2 0.2816 3 0.2503 4 0.1460 5 0.0584 6 0.0162 7 0.0031 8 0.0004 (c) Using the table you selected in part (b) i. What values of X are consistent with the belief that the student is randomly selecting the answers on the exam? ii. What values of X suggest that the student studies for the exam?

Explanation / Answer

b)

Cumilative CDF is given by

1

c)

(i) For the student to be randomly selecting answers the cumilative probability should be 50% or or less

At X=2 cumulative probability=0.3907

At X=3  cumulative probability=0.6488

Hence X=2 is the answer

(ii)

For making sure that the student studies for the exam at 95% confidence

At X=5 cumulative probability=0.9456

At X=6 cumulative probability=0.9857

Hence at X value of 6 and above we can be sure that student has studied for the exam

x P(X=x) CDF 0 0.0317 0.0317 1 0.1267 0.1584 2 0.2323 0.3907 3 0.2581 0.6488 4 0.1936 0.8424 5 0.1032 0.9456 6 0.0401 0.9857 7 0.0115 0.9972 8 0.0024 0.9996 9 0.0004

1

Related Questions

Navigate

• Browse (All)
• Browse 3
• Subjects

---

---

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