Questions: Find the area under the standard normal curve between z=0.02 and z=2.69. Round your answer to four decimal places, if necessary.

Find the area under the standard normal curve between z=0.02 and z=2.69. Round your answer to four decimal places, if necessary.
Transcript text: Save \& Exit Certify Lesson: 6.2 The Standard Normal Distribut... Question 8 of 12 . Step 1 of 1 7/12 Correct Find the area under the standard normal curve between $z=0.02$ and $z=2.69$. Round your answer to four decimal places, if necessary. Answer Table: $\square$ If you would like to look up the value in a table, select the table you want to view, then either click the cell at the intersection of the row and column or use find the appropriate cell in the table and select it using the Space key. Normal Table $-\infty$ to $-z$ Normal Table $-\infty$ to $z$
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Solution

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Solution Steps

Step 1: Define the Problem

We need to find the area under the standard normal curve between \( z = 0.02 \) and \( z = 2.69 \). This area can be expressed as the difference between the cumulative distribution function (CDF) values at these two z-scores.

Step 2: Calculate the CDF Values

The area can be calculated using the formula: \[ P = \Phi(Z_{end}) - \Phi(Z_{start}) \] where \( \Phi(z) \) is the cumulative distribution function of the standard normal distribution.

Step 3: Substitute the Z-scores

Substituting the values into the equation: \[ P = \Phi(2.69) - \Phi(0.02) \]

Step 4: Evaluate the CDF Values

From the calculations, we find: \[ P = 0.4884 \]

Final Answer

The area under the standard normal curve between \( z = 0.02 \) and \( z = 2.69 \) is given by: \[ \boxed{P = 0.4884} \]

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