Answer with explanation please Based on a USA today poll ass

Answer with explanation please

Based on a USA today poll, assume that 10% of the population believes that college is no longer a good investment.

a) Find the probability that among 16 randomly selected people, exactly 4 believe that college is no longer a good investment.
b) Find the probability that among 16 randomly selected people at least 1 believes that college is no longer a good investment.
c) the poll results were obtained by internet users logged on to the USA today website, and the internet users decided wether to ignore the posted survery or respond. What type of sample is this? What does it suggest about the validity of the results?

Solution

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

a)
P( X = 4 ) = ( 16 4 ) * ( 0.1^4) * ( 1 - 0.1 )^12
= 0.0514
b)

P( X < 1) = P(X=0)   
= ( 16 0 ) * 0.1^0 * ( 1- 0.1 ) ^16
= 0.1853
P( X > = 1 ) = 1 - P( X < 1) = 0.8147