Questions: Find the area under the standard normal curve to the right of z=1. A. 0.1587 B. 0.8413 C. 0.1397 D. 0.5398

Solution Steps

We need to find the area under the standard normal curve to the right of \( z = 1 \). This area corresponds to the probability \( P(Z > 1) \), where \( Z \) is a standard normal random variable.

The probability \( P(Z > 1) \) can be expressed using the cumulative distribution function \( \Phi(z) \) of the standard normal distribution: \[ P(Z > 1) = 1 - \Phi(1) \] Alternatively, we can express it as: \[ P(Z > 1) = \Phi(\infty) - \Phi(1) \] where \( \Phi(\infty) = 1 \).

From the calculations, we find: \[ P(Z > 1) = \Phi(\infty) - \Phi(1) = 1 - 0.8413 = 0.1587 \] Thus, the area under the standard normal curve to the right of \( z = 1 \) is \( 0.1587 \).

Final Answer