A random sample of 8 recent college graduates found that starting salaries for computer scientists had a mean of $85000 and a standard deviation of $15000. There are no outliers in the sample data set. Construct a 95% confidence interval for the average starting salary of all computer scientists in gainesville.

(72460, 97540)

Step-by-step explanation:

Given:-

- The sample size, n = 8

- The sample parameters of normal distributed data:

                     mean u = $85000

                     standard deviation s.d = $15000

Find:-

Construct a 95% confidence interval for the average starting salary of all computer scientists in gainesville.

Solution:-

- A random variable (X) denotes average starting salary of all computer scientists in gainesville has a sample normally distribution as follows:

                              X ~ N ( $85000 , $15000^2 )

- The general formulation for CI for known standard deviation with significance α = 1 - 0.95 = 0.05:

                    ( u - Z_a/2*(s.d/√n) < X < u + Z_a/2*(s.d/√n) )

- The Z_a/2 = Z_0.025 = 1.96:

                    ( 85,000 - 1.96*(15,000/√8) < X < 85,000 + 1.96*(15,000/√8) )

                    (72460, 97540)

step-by-step explanation:

milk=16 large

soda=280 kids

juice box=82 regular

63 soda +63 regular

124 large total

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.