Questions: For a standard normal distribution, find: P(z>2.27) Express the probability as a decimal rounded to 4 decimal places.

Solution Steps

We need to find the probability \( P(z > 2.27) \) for a standard normal distribution. This can be expressed using the cumulative distribution function \( \Phi(z) \) as follows:

\[ P(z > 2.27) = 1 - P(z \leq 2.27) = 1 - \Phi(2.27) \]

Using the properties of the cumulative distribution function, we can express the probability as:

\[ P(z > 2.27) = \Phi(\infty) - \Phi(2.27) \]

Where \( \Phi(\infty) = 1 \) since the cumulative probability approaches 1 as \( z \) approaches infinity.

From the calculations, we find:

\[ P(z > 2.27) = 1 - \Phi(2.27) = 0.0116 \]

Final Answer