PROBLEM 4 According to the US Department of Labor, 75% of all adult workers have

Question

PROBLEM 4 According to the US Department of Labor, 75% of all adult workers have a high school diploma. Answer the following questions. Question 16 (2 points): What is the probability that among 16 randomly selected US adult workers 11 have a high school diploma? (Round your answer to 4 places after the decimal point) a) 0.0002 b) 0.0952 c) 0.1802 d) None of the above Question 17 (1 point): How many US adult workers, among 16, are expected to have a high school diploma? a) 7 US adult workers b) 12 US adult workers c) 4 US adult workers d) None of the above Question 18 (1 point): What is the standard deviation of the number of such adults? (Round your answer to 2 places after the decimal point). a) 3.00 US adult workers b) 2.45 US adult workers c) 1.73 US adult workers d) None of the above

Explanation / Answer

16) n = 16

p = 0.75

It is a binomial distribution

P(X = x) = nCx * px * (1 - p)n - x

P(X = 11) = 16C11 * (0.75)^11 * (0.25)^5 = 0.1802

Option - C is correct.

17) Expected number of US adult workers = n * p = 16 * 0.75 = 12

Option - B is correct.

18) Standard deviation = sqrt(n * p * (1 - p))

                                      = sqrt(16 * 0.75 * 0.25)

                                      = 1.73

Option - C is correct

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