A company makes cone-shaped, solid glass paperweights with square photo attached to the base. The paperweights come in a variety of sizes, and the glass used has a density of 3 grams per cubic centimeter. The following expression gives the total
mass of a paperweight with a height of h centimeters and uses 3.14 as an estimate for pi.
3.14h^3– 25.12h^2+ 50.24h
Which of the following is the best interpretation of the factor 3.14(h - 4)^2?

your answer is b.

x = 33.9

y = 65.6

step-by-step explanation:

irst, find the z score of a score of 80. this is given by the formula z = (x-u)/o, where x is the score, u is the mean, and o is the standard deviation. this gives

z = (80-78)/12 = 1/6 = .1667

now, find what percentile a z score of 1/6 correlates to in the normal distribution.

a z score of 1/6 = .1667 is equivalent to the 56.36th percentile of the distribution. so the probability a score is over this is 1-.5636 = .4364

the mean of a sample mean is equal to the original mean. however, the standard deviation of a sample mean is equal to the original standard deviation divided by the square root of n (sample size). so the new standard deviation is 12/sqrt(16) = 3.

the new z score is 80-78/3 = 2/3 = .667. this is equivalent to the 74.86th percentile. so the probability that the mean will be greater than this score is 1-.7486 = .2514.