Question

15.A data set has an AVERAGE = 67 and a STANDARD DEVIATION = 13.

   (A) The data value 44.9 is precisely HOW MANY standard deviations BELOW the average value ?

   (B) A data value happens to be precisely 0.89 standard deviations BELOW its average. WHAT is the Z SCORE for that data value ?

   (C) Please determine the data value which is 2.4 standard deviations ABOVE the mean value.

Answer 1

Solution :

Given that ,

mean = = 67

standard deviation =  = 13

A) x = 44.9

Using z-score formula,

z = x - /   

z = 44.9 - 67 / 13

z = -1.70

-1.70 standard deviation below the average value.

B) 0.89 standard deviation below its average

z-score = -0.89

C) 2.4 standard deviation above the mean value.

z-score = 2.4

Using z-score formula,

x = z * +

x = 2.4 * 13 + 67

x = 98.2

Data value = x = 98.2