Questions: For a standard normal distribution, find: P(z>1.51) Express the probability as a decimal rounded to 4 decimal places.

Solution Steps

We need to find the probability \( P(z > 1.51) \) for a standard normal distribution. This can be expressed using the cumulative distribution function \( \Phi(z) \) as follows:

\[ P(z > 1.51) = 1 - P(z \leq 1.51) = 1 - \Phi(1.51) \]

For our calculation, we identify the Z-scores:

• \( Z_{start} = 1.51 \)
• \( Z_{end} = \infty \)

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

\[ P(z > 1.51) = \Phi(Z_{end}) - \Phi(Z_{start}) = \Phi(\infty) - \Phi(1.51) \]

Since \( \Phi(\infty) = 1 \), we have:

\[ P(z > 1.51) = 1 - \Phi(1.51) \]

From the output, we find:

\[ P(z > 1.51) = 0.0655 \]

Final Answer