A university found that 20 of its student withdraw without c

A university found that 20% of its student withdraw without completing the statistics course. Assume that 20 students registered for the course. (a) compute the probability that two or fewer will withdraw, (b) compute the probability that exactly four will withdraw (c) compute the probability that more than three will withdraw, (d) compute the expected number of withdraws.

Solution

Answer

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

1)

P( X < = 2) = P(X=2) + P(X=1) + P(X=0)   

= ( 18 2 ) * 0.2^2 * ( 1- 0.2 ) ^16 + ( 18 1 ) * 0.2^1 * ( 1- 0.2 ) ^17 + ( 18 0 ) * 0.2^0 * ( 1- 0.2 ) ^18

= 0.2713

2)

P( X = 4 ) = ( 18 4 ) * ( 0.2^4) * ( 1 - 0.2 )^14

= 0.21533

3)

P( X < = 3) = P(X=3) + P(X=2) + P(X=1) + P(X=0)

= ( 18 3 ) * 0.2^3 * ( 1- 0.2 ) ^15 + ( 18 2 ) * 0.2^2 * ( 1- 0.2 ) ^16 + ( 18 1 ) * 0.2^1 * ( 1- 0.2 ) ^17 +

( 18 0 ) * 0.2^0 * ( 1- 0.2 ) ^18 = 0.501

P(X>3) = 1-0.501 = 0.499