Determine the area under the standard normal curve that lies to the right of z = 1.17
To determine the area under the standard normal curve that lies to the right of z = 1.17, we can use a standard normal distribution table or a statistical software.
If you have access to a standard normal distribution table, look up the value corresponding to 1.17 or find the closest value to it. Tables usually provide the cumulative probability to the left of a given z-score. To find the area to the right of z = 1.17, subtract the cumulative probability from 1.
For example, let's say the table gives a cumulative probability of 0.8790 for z = 1.16 and 0.8851 for z = 1.17. So the area to the right of z = 1.17 is:
1 - 0.8851 = 0.1149
Therefore, the area under the standard normal curve to the right of z = 1.17 is approximately 0.1149 or 11.49%.
If you are using statistical software like Excel, Python, or R, you can use the cumulative distribution function (CDF) for the standard normal distribution to calculate the area directly. For example, in Excel, you can use the formula =1 - NORM.S.DIST(1.17, TRUE) to get the same answer.
Remember, the area under the entire standard normal curve is equal to 1.0 or 100%, so the area to the left (cumulative probability) plus the area to the right (which we just calculated) should always equal 1.0.