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

Transcript text: $Z$ is a standard normal random variable. The $\mathrm{P}(z>2.11)$ equals A. 0.0211 B. 0.0174 C. 0.4821 D. 0.9826

Solution

Solution Steps

Step 1: Understanding the Problem

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.

Step 2: Expressing the Probability

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: \[ P(Z > 2.11) = \Phi(\infty) - \Phi(2.11) \]

Step 3: Calculating the Cumulative Probability

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