2. (Binomial dist.) When randomly guessing on a multiple choice test with 8 ques

Question

2. (Binomial dist.) When randomly guessing on a multiple choice test with 8 questions, where each question has 4 options; a) What is the probability that you will get at least 7 questions correct? b) What is the expected number of questions a student will get correct without studying for the exam? c) What is the standard deviation? 3. (Poisson dist.) Surface-finish defects in a small electric appliance occur at random with a mean rate of 0.1 defects per unit. Find the probability that a randomly selected unit will contain at least one surface-finish defect.

Explanation / Answer

2.

a)

Note that P(at least x) = 1 - P(at most x - 1).          
          
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    8      
p = the probability of a success = 1/4 =   0.25      
x = our critical value of successes =    7      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   6   ) =    0.99961853
          
Thus, the probability of at least   7   successes is  
          
P(at least   7   ) =    0.00038147 [ANSWER]

*****************

b)

u = mean = np =    2 [ANSWER]

*******************

c)
  
s = standard deviation = sqrt(np(1-p)) = 1.224744871 [ANSWER]

*******************************************

Hi! Please submit the next part as a separate question. That way we can continue helping you! Please indicate which parts are not yet solved when you submit. Thanks!

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

---

---

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