Question

22. A true-false exam has 54 questions. Use the CLT to approximate the probabil- ity of getting a passing score of 35 or more correct answers simply by guessing on each question.

Answer 1

Soly X~Bln, b) Here n 254 True or False b = P( correct Answer) = £ XN B(54, ) = Use CLT Calculate P(X), 35) =pl X-E(X), 35 "Svits VIX) By CLT, X-Elx) = N(0,1) Svi MO! Elxan pz 54x 227 V(X)2 nb (1-5)= 54x} x { = 27 35- E(X), 35-27 - 2.17 - Ju(x2 / 217-22 pl Movements > Tote = P(22.2-17) = |- P(Z< 2:17) P(X235) - |-$(2-17) where $(-) is CDF of N(0,1) P(X235)= 1-0 (2-1722 1-0.985 PlX235) = 0.015 .015 in