Questions: Find the indicated area under the standard normal curve. To the right of z=2.59 The area to the right of z=2.59 under the standard normal curve is (Round to four decimal places as needed.)

Find the indicated area under the standard normal curve. To the right of z=2.59

The area to the right of z=2.59 under the standard normal curve is
(Round to four decimal places as needed.)

Transcript text: Find the indicated area under the standard normal curve. To the right of $z=2.59$ The area to the right of $z=2.59$ under the standard normal curve is $\square$ (Round to four decimal places as needed.)

Solution

Step 1: Define the Problem

We need to find the area under the standard normal curve to the right of $ z = 2.59 $. This area can be expressed as $ P(Z > 2.59) $.

Step 2: Use the Cumulative Distribution Function

The area to the right of $ z = 2.59 $ can be calculated using the cumulative distribution function (CDF) of the standard normal distribution, denoted as $ \Phi(z) $. The relationship is given by:

\[ P(Z > 2.59) = 1 - \Phi(2.59) \]

Step 3: Calculate the CDF Values

From the output, we have:

\[ \Phi(Z_{end}) = \Phi(\infty) = 1 \] \[ \Phi(Z_{start}) = \Phi(2.59) \approx 0.9952 \]

Thus, we can express the probability as:

\[ P(Z > 2.59) = 1 - 0.9952 = 0.0048 \]

Step 4: Present the Final Result

The area to the right of $ z = 2.59 $ under the standard normal curve is:

\[ \boxed{0.0048} \]

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