Question

A test consists of 30 multiple choice questions, each with five possible answers, only one of which is correct.

Find the mean and the standard deviation of the number of correct answers.

Answer 1

Here we have given that test consist of n = 30 trials, and each having equal probability p =1/5.

since p is the probability of success to correctly attempted options as per given 5 option out of which one is correct.

Each question is nothing but Bernoulli trial with probability p =1/5.

therefore Sn = X1+X2+...+X30 follow the Binomial distribution with parameters(n=30,p=1/5).

therefore Mean of the distribution is np =30*1/5=6

similarly, standard deviation = square root of the variance = (n*p*q)^1/2

= (30*1/5*(1-5))^1/2

=2.19

so the mean and variance are 6 and 2.19 respectively.