Question

Find the z-score that cuts off an area of 0.9798 to the left of the z-score. The values in the table below represent areas to the left of the specified z-score. Round your answer to two decimal places.

a) 2.05
b) 2.08
c) 2.07
d) 2.09

Answer 1

The z-score that cuts off an area of 0.9798 to the left on the standard normal distribution is closest to 2.07, given the options provided.

Step-by-step explanation:

The question is asking to find the z-score that corresponds to an area of 0.9798 to the left of the z-score in a standard normal distribution. To find this z-score, we can look at the provided z-table information and notice that a z-score of 2 yields an area to the left of 0.9772. Given the options, the closest z-score that would provide an area just slightly larger than 0.9772 and therefore be closest to an area of 0.9798 to the left would likely be a z-score between 2 and 2.1. By evaluating the given options, 2.05, 2.07, 2.08, and 2.09, and knowing that a larger z-score results in a larger area to the left, option (c) 2.07 seems to be the best approximation, because it is the smallest increment above 2 and remains under the next full tenth value, which could potentially exceed the desired area.