According to the Department of Labor, 60% of US adult workers have a high school

Question

According to the Department of Labor, 60% of US adult workers have a high school diploma and attended at least some college. Check conditions of Bernoulli Trials and then answer the following questions.

14. Find the Probability that among 15 randomly selected US adult workers 10 have a high school diploma and attended at least some college.

15. How many US adult workers (among 15), on average, are expected to have a high school diploma and attended at least some college?

16. Find the Standard Deviation of such adults.

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 = 10 ) = ( 15 10 ) * ( 0.6^10) * ( 1 - 0.6 )^5
= 0.1859
b.
Mean ( np ) =15 * 0.6 = 9
c.
Standard Deviation ( npq )= 15*0.6*0.4 = 1.8974

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