On a multiple choice test with 29 questions each question ha

On a multiple choice test with 29 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the standard deviation for the number of correct answers. The probability of winning a certain lottery is 1/72,639. For people who play 664 times, find the standard deviation for the number of wins.

Solution

Q52.

Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial

P = One correct among 4 possible answers = 1/ 4 = 0.25
Mean ( np ) =29 * 0.25 = 7.25
Standard Deviation ( npq )= 29*0.25*0.75 = 2.3318