[10 pts.] Consider a binomial experiment with n=20 and p=0.7 a. Compute f(16). b

Question

[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

Explanation / 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

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

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