Unlike scientists or statisticians, economists often break the range of a random variable into five parts, or quintiles. For a standard normal distribution, what is the z-score that defines the second quintile, the 40% point? (a) 0.40 (b) -0.40 (c) 0.253 (d) -0.253 (e) -0.842

(d) -0.253

Step-by-step explanation:

According to a z-score table for a standard normal distribution, a z-score of -0.25 corresponds to the 40.13th percentile, and a z-score of -0.26 corresponds to the 39.74th percentile.

Interpolating those values gives us the z-score for the 40th percentile. The 40.13th percentile is twice as close to the 40th percentile than the 39.74th, thus:

The answer is (d) -0.253.

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.