Questions: Find the area under the standard normal curve between the given z-values. Round your answer to four decimal places, if necessary. z1=-1.57, quad z2=1.57

Find the area under the standard normal curve between the given z-values. Round your answer to four decimal places, if necessary.
z1=-1.57, quad z2=1.57

Transcript text: Find the area under the standard normal curve between the given $z$-values. Round your answer to four decimal places, if necessary. \[ z_{1}=-1.57, \quad z_{2}=1.57 \]

Solution

Solution Steps

Step 1: Calculating the Area to the Left of $z_1$ and $z_2$

Using the standard normal distribution function, the area to the left of $z_1 = -1.57$ is calculated as $0.0582$. Similarly, the area to the left of $z_2 = 1.57$ is $0.942$.

Step 2: Calculating the Area Between $z_1$ and $z_2$

The area between $z_1$ and $z_2$ under the standard normal curve is the difference between the area to the left of $z_2$ and the area to the left of $z_1$, which is $0.942 - 0.0582 = 0.884$.

Step 3: Calculating the Total Area to the Right of $z_2$

The total area to the right of $z_2 = 1.57$ under the standard normal curve is calculated as $1 - 0.942 = 0.0582$.

Final Answer:

The area under the standard normal curve between $z_1 = -1.57$ and $z_2 = 1.57$ is ^0.884^. Additionally, the total area to the right of $z_2 = 1.57$ is ^0.0582^.

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