Questions: Find the indicated area under the standard normal curve. To the left of z=-2.55 and to the right of z=2.55. Click here to view page 1 of the standard normal table. Click here to view page 2 of the standard normal table. The total of the area to the left of z=-2.55 and the area to the right of z=2.55 under the standard normal curve is . (Round to four decimal places as needed.)

Find the indicated area under the standard normal curve. To the left of z=-2.55 and to the right of z=2.55. Click here to view page 1 of the standard normal table. Click here to view page 2 of the standard normal table. The total of the area to the left of z=-2.55 and the area to the right of z=2.55 under the standard normal curve is . (Round to four decimal places as needed.)

Transcript text: Find the indicated area under the standard normal curve. To the left of $\mathrm{z}=-2.55$ and to the right of $\mathrm{z}=2.55$ Click here to view page 1 of the standard normal table. Click here to view page 2 of the standard normal table. The total of the area to the left of $\mathrm{z}=-2.55$ and the area to the right of $\mathrm{z}=2.55$ under the standard normal curve is $\square$ . (Round to four decimal places as needed.)

Solution

Solution Steps

Step 1: Calculate the Probability to the Left of $ z = -2.55 $

To find the area under the standard normal curve to the left of $ z = -2.55 $, we use the cumulative distribution function $ \Phi(z) $:

\[ P = \Phi(Z_{end}) - \Phi(Z_{start}) = \Phi(-2.55) - \Phi(-\infty) = 0.0054 \]

Step 2: Calculate the Probability to the Right of $ z = 2.55 $

Similarly, to find the area to the right of $ z = 2.55 $:

\[ P = \Phi(Z_{end}) - \Phi(Z_{start}) = \Phi(\infty) - \Phi(2.55) = 0.0054 \]

Step 3: Calculate the Total Area

The total area under the standard normal curve to the left of $ z = -2.55 $ and to the right of $ z = 2.55 $ is the sum of the two probabilities calculated:

\[ \text{Total Area} = P(\text{left}) + P(\text{right}) = 0.0054 + 0.0054 = 0.0108 \]