Step 1 :We are asked to find the Z-score such that the area under the standard normal curve to the right is 0.11. This means that we are looking for the Z-score where 11% of the data lies to the right of it.
Step 2 :The Z-score can be found using the inverse of the cumulative distribution function (CDF) of the standard normal distribution. The CDF gives the probability that a random variable is less than or equal to a certain value.
Step 3 :Therefore, to find the Z-score for the area to the right, we need to use 1 - 0.11 = 0.89 as the input to the inverse CDF.
Step 4 :Using the inverse CDF, we find that the Z-score is approximately 1.2265281200366105.
Step 5 :Rounding to two decimal places as needed, the final answer is \(\boxed{1.23}\).