(solve the following problem using integers. show ALL your work.)
1 answer:
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Answer:
0.013 = 1.3% probability that fifteen employees must be tested in order to find three positives.
Step-by-step explanation:
For each employee, there are only two possible outcomes. Either they test positive, or they do not. The probability of an employee testing positive is independent of any other employee, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
40% of the employees have positive indications of asbestos in their lungs
This means that
Find the probability that fifteen employees must be tested in order to find three positives.
2 during the first 14(given by P(X = 2) when n = 14).
The 15th is positive, with 0.4 probability. So
0.0317*0.4 = 0.013.
0.013 = 1.3% probability that fifteen employees must be tested in order to find three positives.