To find the area under the standard normal distribution curve between the z-scores of 2.05 and 2.05, we first need to understand what these z-scores represent.
The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. The z-score indicates how many standard deviations away a particular point is from the mean. In this case, a z-score of 2.05 means that it’s 2.05 standard deviations above the mean.
However, since we are looking for the area between the same z-score (2.05 to 2.05), it basically represents the area of a single point on the curve. The area under the curve at a single point is technically 0, as a precise value does not occupy any measurable area.
To calculate the area under the curve between two different z-scores, we would typically use a z-table or standard normal distribution calculator:
- If we had two different z-scores, we would find the cumulative area up to each z-score and then subtract the smaller area from the larger one.
- However, in this case, since the z-scores are the same, the area is simply 0.
In summary, the area under the standard normal distribution curve between the z-scores of 2.05 and 2.05 is 0.