posted by Christian on .
"A study has shown that 20% of all college textbooks have a price of $90 or higher. It is known that the standard deviation of the prices of all college textbooks is $9.50. Suppose the prices of all college textbooks have a normal distribution. What is the mean price of all college textbooks?"
I have S.D. = 9.5, P = 20% = .2, and I don't know where to go from here. I know the answer is $82 based on a calculator online, but I can't find out how to use the z-table to go from a probability/S.D. to a z-value to plug into X = u + S.D.*z How do I use the z-tables when given a percentage that is outside the bounds of the table? Mine only goes from .1 to .0005, so there are no listed values for .2
Take a z-chart, for example:
20% of all books are $90 or higher, which means 80% of all books are $90 or lower.
Look up the chart for 0-Z (first chart in the above link) for 0.800. You'll find it on the row 0.8, and between columns 0.04 and 0.05 which gives approx. 0.842 SD from the mean after interpolation.
The mean price is therefore $90-0.842*9.5=$82.
what numbers did u plug in for z and x
in the formula z=x-u divided by the s.d