Need with geometry (updated)

what is the value of ac – ef?

m. a. b. c. d. o. e. f. g. h. n

-5. -4. -3. -2. -1. 0 1 2. 3. 4. 5

choices:

a. -5
b. -3
c. -1
d. 1 < correct answer, just took the test

i think it might be 1 but i don't know for sure.

my reasoning:

|-4 - (-2)| - |1-2|
|-4+2| - |-1|
|-2| - |-1|
2 - 1
1

cant open file sorry!

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.