2 15 poists Sally did not study her Introduction to Statisti

2. (15 poists) Sally did not study her Introduction to Statistics material and the Instractor gives a sturpeise quiz. The quiz containa ten multiple choice questins each having four choices and worth 1 point. Assume there is only oe cor anewer. Suppose the breakolown for letter grades is an follows What is the probability that Sally will psss with a B oe better if she guesss i every question?

Solution

This means getting at least an 80, or at lest 8 out of 10.

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 =    10      
p = the probability of a success =    0.25      
x = our critical value of successes =    8      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   7   ) =    0.999584198
          
Thus, the probability of at least   8   successes is  
          
P(at least   8   ) =    0.000415802 [ANSWER]