The mean and the standard deviation of the sampled population are, respectively, 77.4 and 4.0. Find the mean and standard deviation of the sampling distribution of the sample mean x overbar for samples of size n equals 225. Round your answers to one decimal place.

See explanation below.

Step-by-step explanation:

We are looking for the mean and the standard deviation of the sampling distribution of the sample of mean x, given that the mean and standard deviation of sampled population are as follows:

Mean=μ= 77.4

Standard deviation = σ = 4.0

Sample size n = 255

so, the mean of sample mean x will be same as mean of the sampled population:

μₓ = μ = 77.4

and the standard deviation of sample mean x will be standard deviation of the sampled population divided by square root of sample size:

σₓ = σ / √ n

  = 4.0 / √225

= 4.0 / 15

  = 0.3

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.