You enter a walked orchard to pick some mangoes. you picked a few and started to look for the exit. there are three wall each of which has a gate, and at each gate there is a guard. as approach the first gate, the first gate, the guard asks you to give him half the mangoes and then three more. he sends you off, so you approach the second gate and this guard, too, asks you for half of your mangoes and then three more. you move on to the third gate and, once again, the guard asks for half the fruit and three more. he then allows you to exit. you look down in your basket and, sadly, you only have one mangoes left. how many mangoes did you pick up before paying the outrageous tax?

20

step-by-step explanation:

what is the answer?

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.