Determine the area under the standard normal curve that lies to the right of \( (a) Z=0.91 \), (b) \( Z=-0.44 \), (c) \( Z=-1.52 \), and (d) \( Z=-0.82 \). (a) The area to the right of \( Z=0.91 \) is \( \square \). (Round to four decimal places as needed.) (b) The area to the right of \( Z=-0.44 \) is \( \square \). (Round to four decimal places as needed.) (c) The area to the right of \( Z=-1.52 \) is \( \square \). (Round to four decimal places as needed.) (d) The area to the right of \( Z=-0.82 \) is \( \square \). (Round to four decimal places as needed.)

To find the area to the right of the given Z-scores in a standard normal distribution, we can use the cumulative distribution function (CDF) or a standard normal distribution table. Here are the results for each part: (a) For \( Z = 0.91 \): First, find the area to the left of \( Z = 0.91 \), which is approximately 0.8186. To get the area to the right, subtract this from 1. Area = \( 1 - 0.8186 = 0.1814 \). (b) For \( Z = -0.44 \): The area to the left of \( Z = -0.44 \) is approximately 0.3299. Thus, the area to the right is: Area = \( 1 - 0.3299 = 0.6701 \). (c) For \( Z = -1.52 \): The area to the left of \( Z = -1.52 \) is about 0.0643. Therefore, the area to the right is: Area = \( 1 - 0.0643 = 0.9357 \). (d) For \( Z = -0.82 \): The area to the left of \( Z = -0.82 \) is approximately 0.2061. So, the area to the right is: Area = \( 1 - 0.2061 = 0.7939 \). So the answers are: (a) The area to the right of \( Z=0.91 \) is \( 0.1814 \). (b) The area to the right of \( Z=-0.44 \) is \( 0.6701 \). (c) The area to the right of \( Z=-1.52 \) is \( 0.9357 \). (d) The area to the right of \( Z=-0.82 \) is \( 0.7939 \).