The distribution of SAT scores is approximately normal with a mean of 1500. If 1628 is the 90th percentile, what is the standard deviation?

Hello,

Answer

Step-by-step explanation:

p(z<a)=0.9

p(z<1.29)=0.9015

p(z<1.28)=0.8997

using linear interpolation: with 4 decimals

p(z<1.282)<0.9

x = 16

y = 14

Step-by-step explanation:

The figure is a parallelagram.

That means that the diagonals bisect each other.

x = y + 2                  Subtract 2 from both sides

x - 2 = y                   Switch

y = x - 2

y + 10 = 2x - 8         Subtract 10 from both sides

y = 2x - 8  - 10

y = 2x - 18

Now the ys have to be equal so equate the right side of each equation.

2x - 18 = x - 2          Add 18 to both sides

2x = x - 2 + 18

2x = x + 16               Subtract x from both sides

2x - x = 16

x = 16

y = x - 2

y = 16 - 2

y = 14