select-the-choice-that-correctly-describes-three-meanings-of-the-area-under-a-no

Question

Select the choice that correctly describes three meanings of the area under a normal density curve to the left of a point x0x_0.

Accepted Answer

P(X≤x0)=∫−∞x0f(x) dx\displaystyle P(X\le $$x_0$$)=\int_{-\infty}^{$$x_0$$} f(x)\,dx; the area is the percentile rank of x0x_0; the area is the expected proportion of future observations less than or equal to x0x_0.

Answer

P(X≤x0)=∫−∞x0f(x) dx\displaystyle P(X\le $$x_0$$)=\int_{-\infty}^{$$x_0$$} f(x)\,dx; the area equals f(x0)f($$x_0$$); the area equals the interquartile range.

Answer

P(X≤x0)=∫−∞x0f(x) dx\displaystyle P(X\le $$x_0$$)=\int_{-\infty}^{$$x_0$$} f(x)\,dx; the area equals the variance of XX; the area equals the probability density at the mean.

Answer

P(X≤x0)=∫−∞x0f(x) dx\displaystyle P(X\le $$x_0$$)=\int_{-\infty}^{$$x_0$$} f(x)\,dx; the area equals the sample median; the area equals the mode of the sample.