Government data show that 6% of the American population are at least 75 years of age, and that about 51% are women. Is it therefore correct to conclude that because (0.06) * (0.51) = 0.0306, about 3% of the population are women at least 75 years of age? Explain.

Question

Mathematics

Nikolas Kirk

13 March, 10:07

Government data show that 6% of the American population are at least 75 years of age, and that about 51% are women. Is it therefore correct to conclude that because (0.06) * (0.51) = 0.0306, about 3% of the population are women at least 75 years of age? Explain.

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Nathaniel Fischer · Answer 1

It is not correct to conclude that 3% of the population are women at least 75 years of age.

Step-by-step explanation:

To be able to calculate that P (woman and 75 years or greater) = (0.06) (0.51) you would have to know if these events are independent from one another, which we do not know.

To know if these events are independent, we would have to see if the percentage of women over 75 years is 51% compared to men.

Following the same idea, we would also have to see if, considering only the United States women population, the percentage of women over 75 years is also 6% in this subpopulation.

Since we do not have the data to state that these events are independent, conclude that 3% of the population are women at least 75 years of age is not correct.