Problem

Part 4 of 4 Determine the area under the standard normal curve that lies to the right of (a) $Z=-0.25$, (b) $Z=-0.53$, (c) $Z=-0.71$, and (d) $Z=1.35$. Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). (a) The area to the right of $Z=-0.25$ is 0.5987 (Round to four decimal places as needed) (b) The area to the right of $Z=-0.53$ is 0.7019 (Round to four decimal places as needed.) (c) The area to the right of $Z=-071$ is 0.7611 (Round to four decimal places as needed) (d) The area to the right of $Z=1.35$ is (Round to four decimal places as needed.)

Solution

Step 1 :Look up the Z-score in a standard normal distribution table for $Z=-0.25$, which gives a value of 0.4013.

Step 2 :Calculate the area to the right by subtracting the table value from 1: \(1 - 0.4013 = 0.5987\).

Step 3 :\(\boxed{0.5987}\) is the area under the standard normal curve to the right of $Z=-0.25$.

Step 4 :Look up the Z-score in a standard normal distribution table for $Z=-0.53$, which gives a value of 0.2981.

Step 5 :Calculate the area to the right by subtracting the table value from 1: \(1 - 0.2981 = 0.7019\).

Step 6 :\(\boxed{0.7019}\) is the area under the standard normal curve to the right of $Z=-0.53$.

Step 7 :Look up the Z-score in a standard normal distribution table for $Z=-0.71$, which gives a value of 0.2389.

Step 8 :Calculate the area to the right by subtracting the table value from 1: \(1 - 0.2389 = 0.7611\).

Step 9 :\(\boxed{0.7611}\) is the area under the standard normal curve to the right of $Z=-0.71$.

Step 10 :Look up the Z-score in a standard normal distribution table for $Z=1.35$, which gives a value of 0.9115.

Step 11 :Calculate the area to the right by subtracting the table value from 1: \(1 - 0.9115 = 0.0885\).

Step 12 :\(\boxed{0.0885}\) is the area under the standard normal curve to the right of $Z=1.35$.

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