Final answer:
The value of z such that 0.05 of the area lies to the right of z when rounded to two decimal places is approximately 1.64, which is found using a z-table or calculator command invNorm(0.95,0,1) to determine the z-score with 0.95 area to the left.
Step-by-step explanation:
When asked to find the value of z such that 0.05 of the area lies to the right of z, we are looking for the z-score which corresponds to an upper tail area of 0.05 in a standard normal distribution. Using a z-table or calculator, we find that the area to the left for this scenario is 1 - 0.05 = 0.95. Hence, the z value we seek, often denoted as z0.05, is the z-score that has 0.95 of the area to its left. The various choices (a) through (d) represent different z-scores, and using a z-table or calculator (such as the TI-83, 83+, or 84+ calculator command invNorm(0.95,0,1)), we find that z0.05 is approximately 1.645, which would be rounded to 1.64 when rounded to two decimal places.