Having problems reading the z-table. I don't understand how .1500% equates to a 1.04 z-score
Thank you for your help
The .15% is the tail end of the probability distribution.
Probability distributions are such that the total area is 1.0 from Z=-∞ to Z=+∞.
For the normal distribution, Z=0 is at 0.5, which means that the probability of a variable falling above 0 is exactly that of falling below 0.
Here you're looking for the value of Z for which the probability of a variable falling above Z is 0.15, and below is 0.85. So look up the table (below) for Z such that the entries of the table is 0.85, which corresponds to a Z=1.04.
Also, check the little sketch in the following table:
http://www.math.unb.ca/~knight/utility/NormTble.htm
To understand how a z-table works, let's break it down step by step.
1. What is a z-score?
A z-score, also known as a standard score, represents how many standard deviations an observation or data point is from the mean of a distribution. It is calculated by subtracting the mean from the observation and dividing the result by the standard deviation.
2. What is a z-table?
A z-table, or a standard normal distribution table, is a table that provides the area under the standard normal curve for various z-scores. Each entry in the table corresponds to a specific z-score and provides the proportion of the area under the curve to the left of that z-score.
Now, let's address your specific example:
You mentioned that you have a proportion of 0.1500 (which is 15.00%) and want to find the corresponding z-score.
1. Start by finding the z-score in the z-table:
Look for an entry in the z-table that is closest to but less than the given proportion (0.1500 or 15.00%). In this case, we would look for the closest value to but less than 0.1500 in the table.
2. Locate the row and column in the z-table:
Once you find the row and column that correspond to the closest value, read the z-score from the intersection of that row and column. This z-score corresponds to the given proportion.
3. Interpretation:
In your case, you mentioned that the z-score is 1.04. This means that the given proportion (0.1500 or 15.00%) corresponds to a z-score of 1.04.
Keep in mind that z-tables often provide values up to a certain number of decimal places, and the exact value may not be listed. In this case, you may need to estimate or interpolate the value based on the closest entries in the table.
I hope this explanation helps you understand how to read a z-table and interpret the z-score for a given proportion. If you have any further questions or need more clarification, please let me know!