Question

The mean height for American adult men is 5 feet 10 inches (5’10"). The standard deviation is roughly 3 inches. Is a 5’7" man considered abnormally short? Discuss your reasons.

Answer 1

Solution :

Given :

The mean height of an American adult = 5 feet 10 inches

Therefore converting feet into inches,

We know, 1 feet = 12 inches

So, 5 feet = 5 x 12 = 60 inches

The mean height in inches = 60+10

                                             = 70 inches

The standard deviation = 3 inches

x = 5 feet 7 inches

  = 5 x 12 + 7

  = 67 inches

∴ z score = $\frac{x-mean}{sd}$

                $=\frac{67-70}{3}$

                $=\frac{-3}{3}$

                 $=-1$

Therefore, the man's height is 1 standard deviation below mean

Any score above greater than 3 or less than -3 is considered to be an outliner.

Here its only -1 and it is less than -3.

Therefore, the height of the man 5'7'' is not considered abnormally short.