An ecological group suspects lobsters are consuming dangerous levels of mercury in a region of the world. Dangerous levels of mercury are classified when they reach beyond 6.5 parts per million. A random sample of 25 lobsters in the region were tested and the data is shown in the stemplot. Stemplot for Mercury Levels.
2|2 4;
2|;
3|1 4;
3|5 8;
4|0 2;
4|5 6;
5|0 1 3 3 4;
5|6 8 9;
6|3 4;
6|6 7 8;
7|1 2;
7|

Key: 2|2 = 2.2 parts per million

Part A: What proportion of the lobsters in the sample have dangerous levels of mercury in their systems? (4 points)

Part B: Construct and interpret a 95% confidence interval for the mean mercury levels of the lobsters if the sample of 25 lobsters has a mean mercury level of 5.05 parts per million and standard deviation of 1.45 parts per million. (6 points)

Part A: 5 out 25 lobsters have dangerous levels of mercury

Part B: the 95% confidence interval is given by (4.45, 5.65)

since everything is given all I had to do is find the critical value which can be found from the resource packet = 2.064

Using the formula we find 5.05+-2.064*1.45/5 = ( 4.45,5.65)

For this case, we have 95% of confidence that the true mean for the average number of lobsters with dangerous levels of mercury is between 4.45,5.65

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.