Question

The height (in inches) of a random sample of 8 National Basketball Association players is shown below.

x
71
73
74
76
77
78
79
80

12	The height of the shortest player deviates from the mean height by _______ standard deviations.
a	-1.82
b	-1.75
c	-1.68
d	-1.60
13	The height of the tallest player deviates from the mean height by _______ standard deviations.
a	1.47
b	1.41
c	1.36
d	1.28

Answer 1

ANSWER:

MEAN HEIGHT = (71 + 73 + 74 + 76 + 77 + 78 + 79 + 80) / 8 = 76 INCHES

STANDARD DEVIATION: IN ORDER TO FIND THAT WE NEED TO SUBTRACT THE MEAN HEIGHT FROM THE HEIGHT OF EACH PLAYER AND SQUARE IT AND THEN ADD IT AND THEN DIVIDE THE WHOLE NUMBER BY THE TOTAL NO OF PLAYERS AND THEN FIND THE SQUARE ROOT

STANDARD DEVIATION = ((71 - 76)^ 2 + ( 73 - 76) ^ 2 + (74 - 76) ^ 2 + (76 - 76) ^ 2 + (77 - 76 ) ^ 2 + ( 78 - 76) ^ 2 + ( 79 - 76 ) ^ 2 + ( 80 - 76) ^ 2 ) / 8

STD = ( (-5) ^ 2 + (-3)^2 + (-2)^ 2 + (0)^2 + (1) ^ 2 + (2) ^ 2 + (3) ^ 2 + (4) ^ 2 ) / 8

STD = ( 25 + 9 + 4 + 0 + 1 +4 + 9 + 16) / 8 = 68 / 8 = 8.5

STD = SQUARE ROOT OF 8.5 = 3.11

12) HEIGHT OF SHORTEST PLAYER = 71 INCH

MEAN HEIGHT = 76 INCH

DIFFERENCE IN HEIGHT = 71 - 76 = -5

SO, DIFFERENCE IN HEIGHT FROM STANDARD DEVIATION = DIFFERENCE IN HEIGHT / STANDARD DEVIATION = -5 / 3.11 = - 1.6

HENCE THE CORRECT OPTION IS D.

13) HEIGHT OF TALLEST PLAYER = 80 INCH

MEAN HEIGHT = 76 INCH

DIFFERENCE IN HEIGHT = 80 - 76 = 4

SO, DIFFERENCE IN HEIGHT FROM STANDARD DEVIATION = DIFFERENCE IN HEIGHT / STANDARD DEVIATION = 4 / 3.11 = 1.28

HENCE THE CORRECT OPTION IS D.