4. Alex needs to take a multiple choice test to qualify for an internship. He wi

Question

4. Alex needs to take a multiple choice test to qualify for an internship. He will pass if he can answer at least half of the questions correctly. He can take test A that has 20 questions with 5 possible answerso test B that has 16 questions with 4 possible answers. Alex did not study for the test and is planning to answer the questions at random. a. Let Xa be a random variable representing the number of Alex's correct answers on test A. Name the distribution of XA and determine its parameters b. What are Alex's chances of passing test A? What are Alex's chances of passing test B? Which test should he choose?

Explanation / Answer

Ans:

a)XA will have Binomial distribution with parameters

n=20,

p=1/5=0.2

(as there are 5 possible answers,so probability of choosing correct answer=1/5)

b)P(XA=r)=20Cr*0.2r*(1-0.2)20-r

P(pass)=P(XA>=10)=1-P(x<=9)

=1-BINOMDIST(9,20,0.2,TRUE)

=1-0.9974=0.0026

c)

XB will have Binomial distribution with parameters

n=16,

p=1/4=0.25

  P(pass)=P(XB>=8)=1-P(x<=7)   

=1-BINOMDIST(7,16,0.25,TRUE)

=1-0.9729=0.0271

d)As,probability of passing in test B is more than passing in test A,so he should choose test B

Related Questions

Navigate

• Browse (All)
• Browse 4
• Subjects

---

---

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