It is conjectured that an impurity exists in 30% of all drinking wells in a certain rural community. In order to gain some insight into the true extent of the problem, it is determined that some testing is necessary. It is too expensive to test all of the wells in the area, so 10 are randomly selected for testing. What is the PMF of the random variable? What is the probability that exactly 3 wells have the impurity, assuming that the conjecture is correct? What is the probability that more than 3 wells are impure?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
It is conjectured that an impurity exists in 30% of all drinking wells in a certain
rural community. In order to gain some insight into the true extent of the problem, it is determined that some testing is necessary. It is too expensive to test all of the wells in the area, so 10 are randomly selected for testing.
- What is the PMF of the random variable?
- What is the
probability that exactly 3 wells have the impurity, assuming
that the conjecture is correct? - What is the probability that more than 3 wells are impure?
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