Z score explanation for negative and positive z-score tables PDF

Preview

Summary

Z Scores explanation...

Description

Z-SCORES: Detailed exp explanation lanation https://www.ztable.org/how-to-use-z-table/

A z-score is the ‘standard score’. It indicates the number of standard deviations a random value ‘X’ lies from the population mean, μ. A positive z-score lies above the mean, whereas a negative z-score lies below the mean. z-score allows you to calculate the probability of occurrence of a certain event. Moreover, it enables you to compare two scores that are from different normal distributions.

You can find the probability of any value belonging to a statistical sample with a standard normal distribution (Z) by the following steps: See the sign ‘+’ or ‘-‘ o off your z-v z-value. alue. ► If it is a positive value, use positive z-table. ► If it is a negative value, use negative z-table.

Negative zz-score -score table The negative z score table is used to find values to the left of the mean. The table entries represent the area under the bell curve to the left of the ‘z-value’ where z-value occurs before the mean. In simple words, this area contains the values which are less than the mean value.

Positive z-score ta table ble The positive z score table is used to find values to the right of the mean. The table entries represent the area under the bell curve to the left of the ‘z-value’ where z-value occurs after the mean. In simple words, this area contains the values which are greater than the mean value. Let’s practice out using an example to see how it works.

Example Consider a group of 150 applicants who took a Statistics test. Jhona was among the test takers and secured only 400 out of 1000. The average score is 750 (µ) and the standard deviation was 150 (σ). Now, we want to examine the performance of Johna in comparison with her peers.

Let’s calculate the z-score corresponding to Jhona’s actual test score. z=(400-750)/150 z= -2.33 Hence, the z-score for Johna’s test score is -2.33. Since the score is negative, so we can easily tell that she underperformed as compared to her peers. To know the exact percentage of deviation from the average score, you need to use the negative z-table.

Step 1: The first step is to go to the row corresponding to ‘-2.3’.

Step 2: The next step is to go to the column of ‘0.03’

Step 3: See the value at the intersection point of row and column. Step 4: The value is 0.0099

Step 5: Multiply the value with 100 to get the percentage 1. i.e. 0.0099 *100=0.99 2. The percentage is 0.99%.

Understanding the result This result indicates that Johna’s performed better than only 0.01% of the students. 0.01% of 150 students is only 1.5. Since human beings cannot be part, so we will round it to 1. Jhona performed better than 1 student only.

PRACTICE

Question 1: What is p(Z...