The graph of y = 2x2 is transformed into y = -2x2 + 3. Which of the following situations best represents the effect of transformation on the graph of the quadratic function? (Select all that apply). The transformation shifts the graph 3 units up.
The transformation shrinks the graph by a factor of -2.
The transformation vertically stretches the graph by a factor of -2.
The transformation reflects the graph over the x-axis.
The transformation shifts the graph 2 units down.

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.