A literature professor decides to give a 20-questiontrue/false quiz to determine

Question

A literature professor decides to give a 20-questiontrue/false quiz to determine who has read an assigned novel. Shewants to choose the passing grade such that the probability of apassing student who guesses on every question is less than (1/10).What score should she set as the lowest passing grade? *Hint: Use Binomial Distribution A literature professor decides to give a 20-questiontrue/false quiz to determine who has read an assigned novel. Shewants to choose the passing grade such that the probability of apassing student who guesses on every question is less than (1/10).What score should she set as the lowest passing grade? *Hint: Use Binomial Distribution

Explanation / Answer

= 20Ck * 0.5k * 0.5(20-k) (from the binomial distribution formula. Here success andfailure both have a probability of 0.5 and n=20 . )
let m be the cutoff for passing the teacher wants 20Ck *0.5k * 0.5(20-k) from k 0 tom-1< 0.1
This is possible for m = 7 from Binomial distributiontables.
k P(x=k) Cumulative Probability 0 0.0000 0.00002 1 0.00000.00002 2 0.0002 0.00002 3 0.0011 0.00020 4 0.0046 0.00129 5 0.01480.00591 6 0.0370 0.02069 7 0.0739 0.05766 8 0.1201 0.13159 9 0.16020.25172 10 0.1762 0.41190 11 0.1602 0.58810 12 0.1201 0.74828 130.0739 0.86841 14 0.0370 0.94234 15 0.0148 0.97930 16 0.00460.99409 17 0.0011 0.99871 18 0.0002 0.99980 19 0.0000 0.99998 200.0000 1.00000
Hope this helps. Feel free to ask for anyclarifications.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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