138k views
0 votes
Determine what​ z-score(s) correspond(s) to​ less than 2 standard deviations away from the mean​. Then use technology or a standard normal distribution table to find the area between the two​ z-scores. If using the table to find the area between two​ z-scores, first find the area to the left of the smaller​ z-score and to the left of the larger​ z-score. The area between the​ z-scores is the difference between these areas. To convert a decimal to a​ percent, multiply by​ 100%.

1 Answer

3 votes

Final answer:

To find the z-scores less than 2 standard deviations from the mean, you use z-scores of -2 and +2. The Z-table gives areas to the left of these scores, and their difference represents the area between them.

Step-by-step explanation:

The question asks for the z-scores that correspond to less than 2 standard deviations away from the mean in a standard normal distribution. In a standard normal distribution, z-scores of -2 and +2 mark the thresholds of central 95% of the data, according to the empirical rule. To find the area between two z-scores, you look up each z-score in a Z-table to determine the area to the left of each. The area between the z-scores of -2 and +2 can be found by subtracting the area to the left of -2 from the area to the left of +2. According to Z-tables, the area to the left of the z-score -2 is approximately 0.0228 and the area to the left of +2 is approximately 0.9772. The area between these scores, representing the central 95%, is thus 0.9772 - 0.0228, which equals 0.9544, or 95.44% when converted to percentage.

Using the z-table, we can find that the z-score for 2 standard deviations away from the mean is approximately 2.00. To find the area between the z-scores, we can use the z-table to find the area to the left of -2.00 (which is approximately 0.0228) and the area to the left of 2.00 (which is approximately 0.9772). The difference between these areas is approximately 0.9544.

User Jamgreen
by
8.0k points

No related questions found