Z Score Example

Z Score Example Definition: - The units marked on the horizontal axis of the standard normal curve are obtained by z and are called the z score or z value. A specific value of z gives the distance between the mean and the point represented by z in terms of standard deviation. Note: - The values on the right side of the mean are positive and those on the left side are negative. The z score for a point on the horizontal axis gives the distance between the mean and the point represented by z in terms of the standard deviation. Z score formula: - For a normal random variable x, a particular value of x can be converted to its corresponding z value by using the formula Z= (x- )/ Where and are the mean and standard deviation of the normal distribution of x, respectively. Example: - Let x be a random variable with its mean equal to 40 and standard deviation equal to 5. Find the z score for 1) X=49 2) X= 55 Solution: - According to the problem the population mean and standard deviations are 40 and 5 respectively. Hence = 40 and =5. 1) For x= 49, z score =(x-)/ =(49 40) / 5 = 1.80 Therefor z score for x= 49 is 1.80 2) For x= 55 z score =(x-)/ = (55-40) / 5 = 3.00 Therefor z score for x= 55 is 3.00