Suppose ACT Reading scores are normally distributed with a mean of 21 and a standard deviation of 6.1. A university plans to award scholarships to students whose scores are in the top 9%. What is the minimum score required for the scholarship?

the minimum score required for the scholarship is 29.24

Step-by-step explanation:

Since the scores are normally distributed, it follows the central limit theorem. The formula for determining the z score is

z = (x - µ)/σ

Where

x = sample mean

µ = population mean

σ = population standard deviation

Since the university plans to award scholarships to students whose scores are in the top 9%, the scores that would be qualified are scores which are at least 91%(100 - 9 = 91).

Looking at the normal distribution table, the z score corresponding to the probability value of 0.91(91/100) is 1.35

From the information given,

µ = 21

σ = 6.1

Therefore,

1.35 = (x - 21)/6.1

6.1 × 1.35 = x - 21

8.235 = x - 21

x = 8.235 + 21 = 29.24

step-by-step explanation:

de-gf

hj=3x+20

ji=15x-64

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1