The surface of a pedestrian bridge forms a parabola. Let the surface at one side of the bridge be represented by the origin (0,0) and the surface at the other side be represented by (16,0) The center of the bridge is 2 feet higher than each side and can be represented by a vertex of (8,2). Write a function in vertex form that models the surface of the bridge.

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.

3 ft is your answer

d: 0.7(t + 4 + 2) = t .

step-by-step explanation: