Question

About % of the area under the curve of the standard normal distribution is outside the interval z=[−1.61,1.61] z=[-1.61,1.61] (or beyond 1.61 standard deviations of the mean).

Answer 1

The area outside the interval z=[-1.61,1.61] of the standard normal distribution is approximately 13.12%.

Step-by-step explanation:

The area under the curve of the standard normal distribution outside the interval z=[-1.61,1.61] is the complement of the area within that interval. Since the total area under the curve is 1, we can subtract the area within the interval from 1 to find the area outside the interval. To do this, we need to find the z-scores corresponding to -1.61 and 1.61 and then use the standard normal distribution table to find the respective areas. The z-score for -1.61 is approximately -0.0484 and for 1.61 is approximately 0.9464. By subtracting the area between these two z-scores from 1, we can find the area outside the interval.

Area outside interval = 1 - Area between -1.61 and 1.61

Using the standard normal distribution table, the area between -1.61 and 1.61 is approximately 0.8688. Therefore, the area outside the interval is approximately 0.1312 or 13.12%.