Sara is not a good student. Her exam strategy is to rely on luck for the next quiz. The quiz consists of 25 multiple-choice questions. Each question has five possible answers, only one of which is correct. Sara plans to guess the answer to each question. Given a binomial random variable with n=25 and p=0.20, find the following probabilities using the binomial table. 1) Sara gets less or equal than four correct answers. 2) Sara gets less than four correct answers.
is it right to use =BINOM.DIST for these question
I suppose one could use Excel, but the exact and approximate probabilities (according to Mathematica) are $$ \mathbb P(X\leqslant 4) = \sum_{i=0}^4\binom{25}i\left(\frac15\right)^i\left(\frac45\right)^{25-i} = \frac{125370713845530624}{298023223876953125} \approx 0.4206743 $$ and $$ \mathbb P(X< 4) = \sum_{i=0}^3\binom{25}i\left(\frac15\right)^i\left(\frac45\right)^{25-i} = \frac{69735425480065024}{298023223876953125} \approx 0.2339933. $$