Enter the correct answer in the box. Solve the quadratic equation by completing the square. 2x2 + 12x = 66
Fill in the values of a and b to complete the solutions.
X=a-sqrt b
X=a+sqrt b

Interpreting as: X=a-sqrt b X=a+sqrt b

Input:

X = a - sqrt(b) X = a + sqrt(b)

Alternate forms:

{a = (sqrt(b) + 1) X, a = X - sqrt(b), b = 0 ∨ X = -1}

{a = (sqrt(b) + 1) X, a + sqrt(b) = X, sqrt(b) (X + 1) = 0}

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.