The faculty members at McAdenville High School want to determine whether there are enough students to have a Winter Formal. Sixty-three of the 150 students surveyed said they would attend the Winter Formal. Construct and interpret a 99% confidence interval for p.

We are 99% confident that about (31.6 to 52.38) % of population would attend the Winter Formal.

Step-by-step explanation:

Given:

- The sample proportion p = 63 out of 150

- The sample size n = 150

Find:

- The required confidence interval and its interpretation.

Solution:

- To develop CI at 99%, we need Z-score value at significance level a = 1 - CI.

                                a = 1 - 0.99 = 0.01

                       CI:    Z_a/2 = Z_0.005 = 2.58

-The formula for developing the confidence interval for any proportion p is given by:

- We can now determine the 99% confidence interval for p using above expression.

                       p = 63 / 150 = 0.42

                       1-p = 0.58

- We are 99% confident that about (31.6 to 52.38) % of population would attend the Winter Formal.

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it