Consider a truefalse exam with 100 questions If a student ra

Consider a true/false exam with 100 questions. If a student randomly selects an answer for each question, find the probability that the student scores at least 60%

Solution

This happens when he answers at least 60 questions correctly.

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 =    100      
p = the probability of a success =    0.5      
x = our critical value of successes =    60      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   59   ) =    0.971556033
          
Thus, the probability of at least   60   successes is  
          
P(at least   60   ) =    0.028443967 [ANSWER]

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

Hi! In case you use another method (like normal approximation), please resubmit this question and put a note to use the normal approximation. Thanks!