Suppose 180 geology students measure the mass of an ore sample. due to human error and limitations in the reliability of the balance, not all the readings are equal. the results are found to closely approximate a normal curve, with mean 88 g and standard deviation 1 g. use the symmetry of the normal curve and the empirical rule as needed to estimate the number of students reporting readings more than 88 g

Given the total number of students are 180, the mean of data is 88g, and standard deviation is 1g.

A normal curve is a bell-shaped curve with symmetry about the mean and it spreads uniformly on both sides (left side and right side) of the mean.

The empirical rule is also called "68-95-99.7" rule. It says that :-

A) 68% of the data values fall between 1 standard deviation about mean (34% on left side and 34% on right side),

B) 95% of the data values fall between 2 standard deviations about mean (47.5% on left side and 47.5% on right side), and

C) 99.7% of the data values fall between 3 standard deviations about mean (49.85% on left side and 49.85% on right side).

According to distribution of normal curve and "68-95-99.7" empirical rule, we can say 49.85% of data values are above the mean within 3 standard deviations.

So it means 49.85% of total students report readings more than 88g.

Number of students reporting readings more than 88g = 49.85% of 180 = 0.4985 × 180 = 89.73

Hence, approximately 89 students report readings more than mean value.

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.