Give your answers to four decimal places (for example, 0.1234).
(a) Find the area under the standard normal curve to the right of $z=-1.06$.
(b) Find the area under the standard normal curve between $z=1.28$ and $z=2.74$.
Answer
Final Answer: \n(a) The area under the standard normal curve to the right of \(z=-1.06\) is approximately \(\boxed{0.8554}\).\n(b) The area under the standard normal curve between \(z=1.28\) and \(z=2.74\) is approximately \(\boxed{0.0972}\).
Step 1 ：The standard normal curve is a special case of the normal distribution where the mean is 0 and the standard deviation is 1. The area under the curve represents the probability of a random variable falling within a certain range.
Step 2 ：To find the area under the standard normal curve to the right of \(z=-1.06\), we need to calculate the cumulative distribution function (CDF) at \(z=-1.06\) and subtract it from 1. This is because the total area under the curve is 1, and the CDF gives the area to the left of a given \(z\)-score.
Step 3 ：After calculation, the area under the standard normal curve to the right of \(z=-1.06\) is approximately 0.8554277003360904.
Step 4 ：To find the area under the standard normal curve between \(z=1.28\) and \(z=2.74\), we need to calculate the CDF at \(z=1.28\) and \(z=2.74\) and subtract the former from the latter.
Step 5 ：After calculation, the area under the standard normal curve between \(z=1.28\) and \(z=2.74\) is approximately 0.09720060873579162.
Step 6 ：Final Answer: \n(a) The area under the standard normal curve to the right of \(z=-1.06\) is approximately \(\boxed{0.8554}\).\n(b) The area under the standard normal curve between \(z=1.28\) and \(z=2.74\) is approximately \(\boxed{0.0972}\).
