Question

use the ti-84 plus calculator to find the z-scores that bound the middle 96% of the area under the standard normal curve. enter the answers in ascending order and round to two decimal places.

Answer 1

The z-scores that bound the middle 96% of the area under the standard normal curve can be found using the invNorm function on the TI-84 Plus calculator. By inputting invNorm(0.02) and invNorm(0.98), the z-scores of approximately -2.05 and 2.05 are obtained, respectively.

Step-by-step explanation:

To find the z-scores that bound the middle 96% of the area under the standard normal curve using a TI-84 Plus calculator, we use the invNorm function. Since the middle 96% of the area is equidistant from both ends of the curve, we are looking for the z-scores that leave 2% in the tails at both ends, which correspond to areas of 0.02 and 0.98 when moving from the left to the right side of the curve.

Enter invNorm(0.02, 0, 1) to find the z-score on the left side, and invNorm(0.98, 0, 1) to find the z-score on the right side. These functions will return the z-scores which are approximately -2.05 and 2.05, respectively. Hence, the z-scores that bound the middle 96% of the area under the standard normal curve in ascending order are -2.05 and 2.05.

Answer 2

To find the z-scores that bound the middle 96% of the area under the standard normal curve, use the TI-84 Plus calculator or other appropriate commands. The lower z-score is -2.05 and the upper z-score is 1.75. Therefore, the z-scores that bound the middle 96% of the area under the standard normal curve are -2.05 and 1.75.

Step-by-step explanation:

To find the z-scores that bound the middle 96% of the area under the standard normal curve, we can use the TI-84 Plus calculator or other appropriate commands on calculators/computers. The first step is to find the z-score that corresponds to the area to the left of 0.02 (since 96% corresponds to 0.02 on each tail of the curve). Using the invNorm(0.02, 0, 1) command, we get a z-score of approximately -2.05. So, the lower z-score is -2.05.

To find the upper z-score, we subtract the lower z-score from 0 (the total area under the curve) and then subtract 0.02 (from each tail). This gives us an area of 0.96, which corresponds to the z-score. Using the invNorm(0.96, 0, 1) command, we get a z-score of approximately 1.75. So, the upper z-score is 1.75.

Therefore, the z-scores that bound the middle 96% of the area under the standard normal curve are -2.05 and 1.75, in ascending order and rounded to two decimal places.