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 or a statistical calculator. Here's how you can do it:
1. Determine the area on both sides of the distribution that covers the middle 55%. Since we want the middle 55%, we need to find the area inside the distribution curve, which is 1 - 0.55 = 0.45.
2. Divide this area by 2, since we want to find the area on each side of the mean. So, 0.45 / 2 = 0.225.
3. Look up the corresponding z-score for the area in the z-table or use a statistical calculator. In this case, we want to find the z-score that corresponds to an area of 0.225. The z-score corresponding to this area is approximately -0.76.
4. To find the lower bound, subtract the z-score from the mean of the distribution. The mean of the standard normal distribution is always 0. So, the lower bound is 0 - (-0.76) = 0.76.
5. To find the upper bound, add the z-score to the mean of the distribution. The mean of the standard normal distribution is always 0. So, the upper bound is 0 + 0.76 = 0.76.
Therefore, the z-scores that bound the middle 55% of the standard normal distribution are -0.76 (small value) and 0.76 (larger value).