An srs of 430 high school seniors gained an average of ¯x=20.44 points in their second attempt at the sat mathematics exam. assume that the change in score has a normal distribution with standard deviation σ = 52.32. we want to estimate the mean change in score u in the population of all high school seniors, give a 95% confidence interval (a, b) for based on this sample.

( 15.49,25.39)

Therefore at 95% confidence interval (a,b) = ( 15.49,25.39)

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean gain _x = 20.44

Standard deviation r = 52.32

Number of samples n = 430

Confidence interval = 95%

z(at 95% confidence) = 1.96

Substituting the values we have;

+20.44+/-1.96(52.32/√430)

+20.44+/-1.96(2.523)

+20.44+/-4.95

= ( 15.49,25.39)

Therefore at 95% confidence interval (a,b) = ( 15.49,25.39)

answer: (-8,4) are the coordinates of a

step-by-step explanation:

let the side of square abcd is x .

thus the area of square abcd is .

now, by the diagram area of triangle ead= 1/2 × ea × ad = 1/2 × ea × x

( because ad is the side of square)

and, according to the question,

the areas of square abcd and right ead are equal.

⇒

⇒ea=2x

thus, ea: ab=2: 1

therefore, point a divides line segment eb into the ratio 2: 1.

⇒ by sectional formula coordinates of a are,

=

=

=(-8, 4)

thus the coordinates of a are (-8,4)

step-by-step explanation:

6