A Calculus student takes a 20question multiple choice test w

A Calculus student takes a 20-question, multiple choice test with 5 answer choices for each question. Find the probability of getting at least 70% of the questions correct?

Solution

This means at last getting 14 correct.

Here, as there are 5 choices, the probability of a correct answer is

p = 1/5 = 0.2

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 =    20      
p = the probability of a success =    0.2      
x = our critical value of successes =    14      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   13   ) =    0.999998155
          
Thus, the probability of at least   14   successes is  
          
P(at least   14   ) =    0.00000184501 [ANSWER]