Find the z-scores that bound the middle 55% of the standard normal distribution
____ small value
_____ larger value
To find the z-scores that bound the middle 55% of the standard normal distribution, we can use the z-table.
1. First, we need to determine the area under the curve that corresponds to the middle 55%. Since the distribution is symmetrical, we can divide the remaining area outside the middle 55% by 2 to get the tail areas on either side.
Tail Area = (100% - 55%) / 2 = 22.5%
2. Next, we need to find the z-scores corresponding to the tail areas using the z-table.
Looking up the tail area of 22.5% in the z-table, we find the z-score is approximately -0.675.
3. To find the smaller value, we subtract the z-score from the mean of the standard normal distribution, which is 0.
Smaller value = 0 - (-0.675) = 0.675
4. To find the larger value, we add the z-score to the mean.
Larger value = 0 + (-0.675) = -0.675
Therefore, the z-scores that bound the middle 55% of the standard normal distribution are approximately 0.675 (smaller value) and -0.675 (larger value).