SOLUTION: A city mayor in Michigan is planning the number of new snow plows he must purchase to remove the snow next winter. The average snowfall in the past 10 years has been normally distr

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Question 1170523: A city mayor in Michigan is planning the number of new snow plows he must purchase to remove the snow next winter. The average snowfall in the past 10 years has been normally distributed with a mean of 112 inches and a standard deviation of 14 inches. What amount, in inches, separates the lowest 20% of the distribution of yearly snowfall in the past 10 years from the highest 20%.
Use the z-table below:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
mean = 112
standard deviation = 14
bottom 20% would have a z-score of -.8416212335
top 20% would have a z-score of .8416212335
uswe the z-score formula to find the raw score.
the z-score formula ia:
z = (x - m) / sd
x = the raw score
m = the mean
sd = the standard deviation.

with your numbers, ...
the low z-score formula is:
-.8416212335 = (x - 112) / 14
solve for x to get:
x = 14 * -.8416212335 + 112 = 100.2173027

the high z-score formula is:
.8416212335 = (x - 112 / 14
solve for x to get:
x = 14 * .8416212335z + 112 = 123.7826973

the amount in inches that separates the lowest 20% of the normal distribution from the highest 20% of the normal distribution is equal to 123.7826973 minus 100.2173027 = 23.56539454 inches.

you have .6 of the area under the normal distribution curve between those 2 z-scores and you have .4 of the area under the normal distribution curve outside of those 2 z-score values.

pictures of the z-score distributions and the raw score distributions are shown below.