Questions: Find the area under the standard normal distribution curve between z=-2.49 and z=1.13. Use The standard Normal Distribution Table and enter the answer to 4 decimal places. The area between the two z values is

Find the area under the standard normal distribution curve between z=-2.49 and z=1.13. Use The standard Normal Distribution Table and enter the answer to 4 decimal places. The area between the two z values is
Transcript text: Find the area under the standard normal distribution curve between $z=-2.49$ and $z=1.13$. Use The standard Normal Distribution Table and enter the answer to 4 decimal places. The area between the two $z$ values is $\square$
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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 distribution curve between the z-scores \( z = -2.49 \) and \( z = 1.13 \). This area can be expressed as:

\[ P = \Phi(Z_{end}) - \Phi(Z_{start}) \]

where \( \Phi \) is the cumulative distribution function (CDF) of the standard normal distribution.

Step 2: Calculate the CDF Values

Using the z-scores provided:

  • For \( Z_{end} = 1.13 \): \[ \Phi(1.13) \approx 0.8644 \]

  • For \( Z_{start} = -2.49 \): \[ \Phi(-2.49) \approx 0.0064 \]

Step 3: Compute the Area

Now, we can compute the area between the two z-scores:

\[ P = \Phi(1.13) - \Phi(-2.49) = 0.8644 - 0.0064 = 0.8580 \]

Final Answer

The area between the two z values is

\[ \boxed{0.8580} \]

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