Final answer:
To find the percent of a standard normal distribution in each region, we can use the cumulative distribution function (CDF) of the standard normal distribution. The CDF gives the probability that a random variable from the standard normal distribution is less than or equal to a given value. We can use a graph of the standard normal distribution to visually represent the percent in each region.
Step-by-step explanation:
To find the percent of a standard normal distribution in each region, we can use the cumulative distribution function (CDF) of the standard normal distribution. The CDF gives the probability that a random variable from the standard normal distribution is less than or equal to a given value. We can use a graph of the standard normal distribution to visually represent the percent in each region.
For example, to find the percent in the middle 20 percent, we subtract the area in the tails from 1 (since the total area under the curve is 1). In this case, the area in each tail is 0.40, so the percent in the middle 20 percent is 1 - 0.40 - 0.40 = 0.20 or 20%.
To find the percent in each tail, we can use z-scores. For the 40th percentile (k1), we find the z-score such that the area to the left of it is 0.40. Using a probability table or calculator, we find that the z-score is approximately -0.25. Similarly, for the 60th percentile (k2), we find the z-score such that the area to the left of it is 0.60. Using a probability table or calculator, we find that the z-score is approximately 0.25.