10 pts Consider a binomial experiment with n20 and p07 a Com

[10 pts.] Consider a binomial experiment with n=20 and p=0.7

a. Compute f(16).

b. Compute p(x16).

c. Compute p(x15).

d. Compute E(x)

e. Compute Var(x) and

2. [10 pts.] In San Francisco, 30% of workers take public transportation daily.

a. In a sample of 10 workers, what is the probability that exactly 3 workers take public transportation daily?

b. In a sample of 10 workers, what is the probability that at least 3 workers take public transportation daily?

3. [10 pts.] The Census Bureau’s Current Population Survey shows that 28% of individuals, ages 25 and older, have completed four years of college. For a sample of 15 individuals, ages 25 and older, answer the following questions:

a. What is the probability four will have completed four years of college?

b. What is the probability three or more will have completed four years of college

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 = 16 ) = ( 20 16 ) * ( 0.7^16) * ( 1 - 0.7 )^4
= 0.1304

b)
P( X > = 16 ) = P(X = 20) + P(X=19) + P(X=18) + P(X=17) + P(X=16) = 0.2375

c)
P( X < = 15) = 1 - P( X > = 16 ) = 1 - 0.2375 = 0.7625

d)
E(X) = 20 * 0.7 = 14

e)
Standard Deviation ( npq )= 20*0.7*0.3 = 2.0494