The average price of gasoline lately has been hovering lately at $3.80. What is the standard deviation if the probability that a gallon of gas costs less than $3.00 is 15%?
One of my favourite webpages
http://davidmlane.com/normal.html
click on "area from a value" below the graph
in "mean" enter 3.8
click on "below" and enter 3
enter some value into mean and look at the bottom output (the probability)
I started with SD of 1 and got .21899..
As I increased the SD this number got bigger, so I started to decrease the SD
at SD = .7 I got .1264.. , getting close to .15
after playing around a bit I found
SD = .772 gave me exactly .15
another way to go:
go to your tables and find .15 in the main body of the chart
you should be between -1.03 and -1.04
take the average:
so the z score = -1.035
-1.035 = (3 - 3.8)/sd
- 1.035sd = -.8
sd = -.8/-1.035 = .7729
close to the .772 which the computer applet gave me.