Problem

Find the area under the standard normal curve to the left of $z=-2.03$ and to the right of $z=1.32$. Round your answer to four decimal places, if necessary.
Answer
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Normal Table $-\infty$ to $-z$
Normal Table $-\infty$ to $z$

Answer

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Answer

\(\boxed{0.1146}\) is the area under the standard normal curve to the left of \(z=-2.03\) and to the right of \(z=1.32\).

Steps

Step 1 :We are asked to find the area under the standard normal curve to the left of \(z=-2.03\) and to the right of \(z=1.32\). This is the sum of the two areas.

Step 2 :We can find these areas using the cumulative distribution function (CDF) of the standard normal distribution. The CDF at \(z\) is the area to the left of \(z\). So, the area to the right of \(z\) is \(1 - \text{CDF}(z)\).

Step 3 :Calculate the area to the left of \(z=-2.03\) using the CDF. The result is approximately 0.0212.

Step 4 :Calculate the area to the right of \(z=1.32\) using \(1 - \text{CDF}(z)\). The result is approximately 0.0934.

Step 5 :Add the two areas together to get the total area under the curve. The result is approximately 0.1146.

Step 6 :\(\boxed{0.1146}\) is the area under the standard normal curve to the left of \(z=-2.03\) and to the right of \(z=1.32\).

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