Question

Explain Z Value with an Example and Graph. PLEASE SHOW DETAIL OF YOUR SET UP, FORMULA, CALCULATION. NO EXCEL! Thank you!

Answer 1

Solution:

Z-value helps in finding what percentage is under the curve at any particular point. It is called a standard score. The area under the whole normal distribution curve is 1. The Z-score is calculated using the formula

Where is the population mean and

is the population standard deviation.

From the graph we can observe that 68.27% of the observation lies within 1 standard deviation from the mean, 95.45% of the observation lies within 2 standard deviation from the mean and 99.73% of the observation lies within 3 standard deviation from the mean.

Example - The mean score for a class of 60 students is 70 and the standard deviation is 15 marks. A student named Amy asked the teacher if by scoring 80 she has performed well or not. The Z-score would be

Z = (80 - 70)/15

Z = 0.67