Problem

Find the area under the standard normal curve from 0 to the indicated value of $z$.
\[
0.85
\]
A. 0.3023
B. 0.8023
C. 0.1977
D. 0.6977

Answer

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Answer

Final Answer: The area under the standard normal curve from 0 to 0.85 is approximately \(\boxed{0.8023}\).

Steps

Step 1 :The area under the standard normal curve from 0 to a given value of $z$ is given by the cumulative distribution function (CDF) of the standard normal distribution at $z$. The CDF of the standard normal distribution at $z$ is given by \(\Phi(z) = \frac{1}{2}[1 + \text{erf}(z/\sqrt{2})]\), where \(\text{erf}\) is the error function.

Step 2 :Substitute $z$ = 0.85 into the formula, we get \(\Phi(0.85) = \frac{1}{2}[1 + \text{erf}(0.85/\sqrt{2})]\).

Step 3 :Calculate the above expression to get the area under the curve from 0 to 0.85, which is approximately 0.8023374568773076.

Step 4 :Final Answer: The area under the standard normal curve from 0 to 0.85 is approximately \(\boxed{0.8023}\).

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