Questions: Z is a standard normal random variable. The P(z>2.11) equals A. 0.0211 B. 0.0174 C. 0.4821 D. 0.9826

Solution Steps

We need to find the probability $P(Z > 2.11)$ where $Z$ is a standard normal random variable. This can be expressed in terms of the cumulative distribution function $\Phi$ of the standard normal distribution.

The probability can be rewritten using the cumulative distribution function as follows: $$P(Z > 2.11) = 1 - P(Z \leq 2.11) = 1 - \Phi(2.11)$$ Since $\Phi(\infty) = 1$, we can express this as: $$P(Z > 2.11) = \Phi(\infty) - \Phi(2.11)$$

From the output, we have: $$P(Z > 2.11) = \Phi(\infty) - \Phi(2.11) = 0 - 0.9826 = 0.0174$$

Final Answer