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Answer:
3.54% probability of observing at most two defective homes out of a random sample of 20
Step-by-step explanation:
For each house that this developer constructs, there are only two possible outcomes. Either there are some major defect that will require substantial repairs, or there is not. The probability of a house having some major defect that will require substantial repairs is independent of other houses. So we use the binomial probability distribution 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.
30% of the houses this developer constructs have some major defect that will require substantial repairs.
This means that
If the allegation is correct, what is the probability of observing at most two defective homes out of a random sample of 20
This is when n = 20. So
3.54% probability of observing at most two defective homes out of a random sample of 20