A simple random sample of 35 colleges and universities in the United States has a mean tuition of $19,400 with a standard deviation of $11,000. Construct a 90% confidence interval for the mean tuition for all colleges and universities in the United States. Round the answers to the nearest whole number A 90% confidence interval for the mean tuition for all colleges and universities is < μ <.

$16,341< μ <$22,459.

Step-by-step explanation:

The formula for calculating confidence interval is expressed as;

CI = xbar±(z×s/√n)

xbar is the mean tuition

z is the z score at 90% CI

s is the standard deviation

n is the sample size

Given

xbar = $19,400

s = $11,000

n = 35

z = 1.645

Substitute into the formula for calculating confidence interval

CI = xbar±(z×s/√n)

CI = 19400±(1.645×11000/√35)

CI = 19400±(1.645×11000/5.916)

CI = 19400±(1.645×1859.36)

CI = 19400±3058.65

CI = [19400-3,058.65, 19400+3,058.65]

CI = [16,341.35, 22,458.65]

CI = [16,341, 22,459] to nearest whole number.

Hence a 90% confidence interval for the mean tuition for all colleges and universities is 16,341< μ <22,459.

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this