5 Sally did not study her Introduction to Statistics materia

5. Sally did not study her Introduction to Statistics material and the Instructor gives a surprise quiz. The quiz contains ten multiple choice questions, each having four choices and worth 1 point. Assume there is only one correct answer. Suppose the breakdown for letter grades is as follows: What is the probability that Sally will pass with a B or better if she guesses on every question?

Solution

To pass with at least B, he should get 8 or more correct.

Note that

P(8 or more) = 1 - P(7 or less)

Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    10      
p = the probability of a success =    0.25      
x = the number of successes =    7      
          
Then the cumulative probability is          
          
P(x <=   7   ) =    0.999584198
          
          
Thus, the probability of 8 or more is  

P(8 or more) = 0.000415802