1. The length of human pregnancies from conception to birth is normally
distributed with mean 260 days and standard deviation 15 days. Use
the 68-95-99.7 rule and also using Z scores to estimate the following
to confirm the answers. Use both methods if possible and show all
detailed steps. Draw a distribution graph to clearly depict the
distributions in both cases, clearly showing the mean and standard
deviation in each case.
a. The proportion of the lengths of pregnancies that fall below 245 days
b. The proportion of the lengths of pregnancies that fall below 275 days
c. The proportion of the lengths of pregnancies that fall between 230 days and 275 days.
d. The middle 95% of the lengths of all pregnancies fall between which
two values?
e. How short must the length of a pregnancy is for it to fall in the shortest
2.5% of all human pregnancies?
f. How long must the length of a pregnancy for it to fall in the longest
2.5% of all human pregnancies?

were is the equation

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.

answer: the answer is e

step-by-step explanation:

1260=3*6*7*10=3^2*2^2*7*5 perfect cude = 3^3*2^

step-by-step explanation: