The shape of the distribution of the time required to get an oil change at a 10-minute oil-change facility is unknown. However, records indicate that the mean time is 11.9 minutes, and the standard deviation is 4.8 minutes.
Complete parts (a) through (c):
(a) To compute probabilities regarding the sample mean using the normal model, what size sample would be required?

A. The normal model cannot be used if the shape of the distribution is unknown.
B. The sample size needs to be less than or equal to 30.
C. The sample size needs to be greater than or equal to 30.
D. Any sample size could be used.

(b) What is the probability that a random sample of n 35 oil changes results in a sample mean time less than 20 minutes? (Round to four decimal places as needed.)
(c) Suppose the manager agrees to pay each employee a $50 bonus if they meet a certain goal. On a typical Saturday, the oil-change facility will perform 35 oil changes between 10 A. M. and 12 P. M. Treating this as a random sample, there would be a 10% chance of the mean oil-change time being at or below what value?

a variable is any characteristics, number, or quantity that can be measured or counted. a variable may also be called a data item. hope i !

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.

its the second choice.

step-by-step explanation:

the elements in the range will be 7 less than the elements in the domain.

-2x-4

step-by-step explanation: