statistics HW: A multiple-choice text consists of 30 questio

[rfimbres]

A multiple choice test consists of 30 questions with the possible answers a, b, c, d, and e. Estimate the probability that, with random guessing, the number of correct answers is between 4 and 15, inclusive.

 

[pka]

\(\displaystyle \L \sum\limits_{k = 4}^{15} {\left( {\begin{array}{c}
{30} \\
k \\
\end{array}} \right)\left( {\frac{1}{5}} \right)^k \left( {\frac{4}{5}} \right)^{30 - k} } .\)