Given that Z is a standard normal random variable, which of the following best describes the area to the left of a value z?
A) P(Zz)
B) P(Zz).
C) P(0Zz)
D) P(Z-z)

Question

Quizplus · Accepted Answer

The area to the left of a value z on a standard normal distribution is the cumulative probability up to that value, which is represented by P(Z<z). Since z is not included in the area, it should be a strict inequality, giving us P(Z<z). Option A has an incorrect inequality (greater than or equal to instead of strictly less than), Option C has unnecessary terms (0 and z), and Option D has an incorrect inequality (less than instead of less than or equal to). Therefore, the only correct option is B, which represents the area to the left of z on a standard normal distribution as P(Z<z).

Given That Z Is a Standard Normal Random Variable, Which