Imagine that Exam 1 for Statistics 2160 this term will have

Imagine that Exam 1 for Statistics 2160 this term will have 62 questions. Each question has 5 multiple choice options, giving you a probability of 0.2 of getting each question right purely by guessing. Assuming that you guess on all questions, what is the probability that you get greater than 15 questions right on your exam?

If possible, explain answer if you can use a TI-84 calculator to get answer.

Solution

Note that P(more than x) = 1 - P(at most x).          
          
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    62      
p = the probability of a success =    0.2      
x = our critical value of successes =    15      
          
Then the cumulative probability of P(at most x) from a table/technology is          
          
P(at most   15   ) =    0.838086607
          
Thus, the probability of at least   16   successes is  
          
P(more than   15   ) =    0.161913393 [ANSWER]

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You can calculate P(at most 15) using

binomcdf(62,0.2,15)

Then get its complement to get the answer.