Find the indicated z-scores shown in the attached graph. First note that the shaded region is an area in between two z-scores. This means that the region is not a cumulative area from the left and to solve requires working instead with regions that are cumulative areas from the left. Thus, to find the z-scores in this situation, one needs to find the cumulative areas to the left of each unknown z-score. While either the Standard Normal Table or technology can be used to find the corresponding z-score, in this problem, use the table. The two values must be approached individually. First, consider the z-score for the lower 0.4649 to the left of z=0. The area to the left of this z-score is not given in the problem directly and must be found using the inner areas given. Note that 0.5 of any Standard Normal Distribution lies to the left of z=0 and that each half is divided into two unequal regions by the unknown z-scores. The larger region is known from the problem statement to be 0.4649 and the smaller region is the one to the left of the desired z-score. If the region of this area is known, then the Standard Normal Table can be used to find the z-score. Using the fact that 0.5 of the distribution lies to the left of z=0, this smaller region is 0.5 − 0.4649 = _____. Using the cumulative area from the left, locate the closest area in the body of the Standard Normal Table and identify the z-score corresponding to the lower _. Round the value to the nearest two decimal places. The z-score for the lower 0.0351 is _. To find the second z-score, find the total cumulative area to the left of the upper z-score. This is found by summing the three regions to the left of the z-score. The first two larger regions are given in the problem statement as 0.4649 each. The third region was found earlier to be _ when determining the first z-score. Thus, the sum of these three regions is 0.4649 + 0.4649+ _ = ? Now, find the z-score corresponding to _ in the Standard Normal Table. Round the value to the nearest two decimal places. z≈ 1.81 Therefore, the z-scores are approximately _ and ______???

Question

Find the indicated z-scores shown in the attached graph.

First note that the shaded region is an area in between two z-scores. This means that the region is not a cumulative area from the left and to solve requires working instead with regions that are cumulative areas from the left.

Thus, to find the z-scores in this situation, one needs to find the cumulative areas to the left of each unknown z-score.

While either the Standard Normal Table or technology can be used to find the corresponding z-score, in this problem, use the table.

The two values must be approached individually.

First, consider the z-score for the lower 0.4649 to the left of z=0.

The area to the left of this z-score is not given in the problem directly and must be found using the inner areas given.

Note that 0.5 of any Standard Normal Distribution lies to the left of z=0 and that each half is divided into two unequal regions by the unknown z-scores.

The larger region is known from the problem statement to be 0.4649 and the smaller region is the one to the left of the desired z-score.

If the region of this area is known, then the Standard Normal Table can be used to find the z-score.

Using the fact that 0.5 of the distribution lies to the left of z=0, this smaller region is 0.5 − 0.4649 = _________.

Using the cumulative area from the left, locate the closest area in the body of the Standard Normal Table and identify the z-score corresponding to the lower _________.

Round the value to the nearest two decimal places.

The z-score for the lower 0.0351 is _________.

To find the second z-score, find the total cumulative area to the left of the upper z-score.

This is found by summing the three regions to the left of the z-score.

The first two larger regions are given in the problem statement as 0.4649
each.

The third region was found earlier to be _________ when determining the first z-score.

Thus, the sum of these three regions is 0.4649 + 0.4649+ _________ = ?

Now, find the z-score corresponding to _________ in the Standard Normal Table. Round the value to the nearest two decimal places.

z≈ 1.81

Therefore, the z-scores are approximately _________ and __________???