For a normal distribution,
a. what z-score separates the highest 10% from the rest of the scores?
b. what z-score separates the highest 30% from the rest of the scores?
c. what z-score separates the lowest 40% from the rest of the scores?
d. what z-score separates the lowest 20% from the rest of the scores?

1.282, -0.5244,...

Step-by-step explanation:

We know that Z is a standard normal variate with mean =0, and std dev =1

a) z-score separates the highest 10% from the rest of the scores

= 90th percentile = 1.282

b) z-score separates the lowest 30% from the rest of the scores

= 30th percentile = -0.5244

c) z-score separates the lowest 40% from the rest of the scores

= 40th percentile = -0.2533

d) z-score separates the lowest 20% from the rest of the score

=20th percentile = -0.8416

chicken chicken chicken

step-by-step explanation:

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form