A rocking chair rocks back and forth. As it rocks, the distance from the wall to the back of the
chair changes sinusoidally. When the chair rocks away from the wall it is at a max distance of 40
cm from the wall, when it rocks towards the wall it gets to a minimum distance of 6 cm. How far
from the wall is the back of the chair when the chair is not moving?

answer: finding the extract measurements and knowing the points

step-by-step explanation:

answer: your answer is c

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.