Determine the area under the standard normal curve that lies to the right of \( (a) Z=1.63 \), (b) \( Z=1.13 \), (c) \( Z=-0.77 \), and (d) \( Z=0.11 \). (a) The area to the right of \( Z=1.63 \) is \( \square \). (Round to four decimal places as needed.)

To find the area under the standard normal curve to the right of a given Z value, you typically look up the Z value in a standard normal distribution table or use a calculator that provides cumulative distribution function (CDF) values. The cumulative area to the left of the Z value can be subtracted from 1 to find the area to the right. Let's calculate those areas: (a) For \( Z=1.63 \): - The cumulative area to the left is approximately 0.9484. - Therefore, the area to the right is \( 1 - 0.9484 = 0.0516 \). (b) For \( Z=1.13 \): - The cumulative area to the left is approximately 0.8708. - Hence, the area to the right is \( 1 - 0.8708 = 0.1292 \). (c) For \( Z=-0.77 \): - The cumulative area to the left is approximately 0.2206. - Thus, the area to the right is \( 1 - 0.2206 = 0.7794 \). (d) For \( Z=0.11 \): - The cumulative area to the left is approximately 0.5438. - Consequently, the area to the right is \( 1 - 0.5438 = 0.4562 \). Now to summarize the answers: (a) The area to the right of \( Z=1.63 \) is \( 0.0516 \). (b) The area to the right of \( Z=1.13 \) is \( 0.1292 \). (c) The area to the right of \( Z=-0.77 \) is \( 0.7794 \). (d) The area to the right of \( Z=0.11 \) is \( 0.4562 \).