Answer :
Final answer:
Using the binomial probability formula, the probability that out of 20 workers exactly 15 turn out to be satisfactory for a company that finds 1 out of every 5 workers as unsatisfactory is approximately 0.01456.
Explanation:
This problem is best solved using the binomial probability formula which is P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k)). Here n is the number of trials, k is the number of successes we want, p is the probability of one success, and C(n, k) is the binomial coefficient or combinations of 'n' choose 'k'.
Given in the question, one out of every 5 workers is unsatisfactory, thus the probability of one worker being satisfactory (p) is 4/5 or 0.8. We have total 20 workers (n) and we are looking for the scenario where exactly 15 of them are satisfactory (k).
Substituting these values into the formula, we can calculate the binomial probability. After calculation, the probability that exactly 15 workers out of 20 are satisfactory is approximately 0.01456.
So the answer is d) 0.01456.
Learn more about Binomial Probability here:
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