Expert: Paul Klarreich - 4/27/2011

Question
A Bio tutor recorded the lung capacity of each 16-year-old in her school.The tutor determined that the values were normally with a mean of 3500mL and a standard deviation of 300 mL. If 23% of the 16-year-olds' lung capacities were less than Samantha's, what is Samantha's lung capacity? I am supposed to round my answer upto the nearest millilitre.

Answer
Questioner:   Andrea
Category:  Advanced Math
Private:  No
 
Subject:  Probability and Statistics
Question:  A Bio tutor recorded the lung capacity of each 16-year-old in her school.The tutor determined that the values were normally DISTRIBUTED with a mean of 3500mL and a standard deviation of 300 mL. If 23% of the 16-year-olds' lung capacities were less than Samantha's, what is Samantha's lung capacity? I am supposed to round my answer upto the nearest millilitre.
 
Let's reword:

A set of values are normally distributed with a mean = 3500 mL and a standard deviation = 300.  What data value has a percentile of 0.23?

From:

http://www.mathsisfun.com/data/standard-normal-distribution-table.html

you will find a 'tail' of 0.23, or a 'central piece' of 0.27, which corresponds to about z = 0.74, which means, since you want the left side, 0.74 times the s.d. of....

I think you can finish now.