According to the data, the mean quantitative score on a standardized test for female college-bound high school seniors was 500. The scores are approximately Normally distributed with a population standard deviation of 50. A scholarship committee wants to give awards to college-bound women who score at the 99th percentile or above on the test. What score does an applicant need? Include a well-labeled Normal curve as part of your answer.

Step-by-step explanation:

Hello!

The variable of interest is X: Score that a female college student obtained in a standardized test.

This variable has an approximately normal distribution with standard deviation σ= 50 and mean μ= 500

You need to find the score value that marks the 99th percentile, meaning that it separates 99% of the distribution from the top 1%, symbolically:

P(X≥x₀)= 0.01 or P(X≤x₀)= 0.99

Using the standard normal distribution Z=(X-μ)/σ ≈ N(0;1) you have to use the standard normal distribution to find the corresponding value.

first using the Z-table you have to look the Z value that accumulates 0.99 of distribution:

z₀= 2.334

Using the Z formula and the known values of μ and σ you can clear the value of x₀

z₀= (x₀-μ)/σ

z₀*σ= x₀-μ

x₀= (z₀*σ) + μ

x₀= (2.334*50)+500= 616.7

The college student has to become a score of 616.7 or more to receive the award.

I hope it helps!

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is