In a random survey of 3,015 boys age 11, the average height was 146 cm, and the standard deviation (SD) was 8 cm. A histogram suggested the heights were approximately normally distributed. One boy was 170 cm tall. He was above average by SDs.

The boy was above average  by 3 SDs.

i.e. 3*SD=3*8=24 cm above the average value.

Step-by-step explanation:

Given:

3015 boys with age of 11 ,Avg height of 146 cm and Standard deviation of 8 cm.

To find:

How above Avg 170 cm tall boy is?

Solution:

The mean of 3015 boys  is of 146 cm in height,

And standard deviation is 8cm.

the height of one boy is 170 cm ,

This boy's height is 24 cm above the  average height.

i.e. 170 cm -146cm=24 cm.

Hence , standard deviation is of 8cm .

1 SD=8cm

2SD=8+8=16 cm

3SD= 8+8+8=24 cm.

The height of boy  in compare of standard deviation=24/8 .

=3

Hence  the height of the boy 3 times the standard deviation ,170cm.

Let a be an integer. if a=0mod4, a^2=0mod4if a=1mod4, a^2=1mod4if a=2mod4, a^2=0mod4if a=3mod4, a^2=1mod4note that a square number is either 0mod4 or 1mod4.let x, y be two odd numbers.consider the following 4 cases: (i) x=1mod4 and y=1mod4, (ii) x=1mod4 and y=3mod4, (iii) x=3mod4 and y=1mod4(iv) x=3mod4 and y=3mod4in any cases, (x^2)+(y^2)=2mod4, which cannot be a square number.