If 23% of the 16-year-olds' lumg capacites were less han samantha's, wha is samantha's lumg capacity?
A biology teacher recorded the lung capacity of each 16-year-old in her school. the teacher determind that the values were normally distributed with a mean of 3500 mL and a standard deviation of 300mL.
We need the z-table to calculate this.
`z = (x-mu)/sigma`
If you refer to a z-table you would find that 23rd percentile lies with the z-value of -0.74. (you have to go backwards from the centerline, z= 0).
`-0.74 = (x-3500)/300`
`x-3500 = -222`
`x = 3500-222`
`x = 3278 ml.`
Therefore Samantha's lung capacity is 3278 ml.
I think I would solve this with the normal distribution:
surface left: 23% = 0,23
(surface right: 1 - 0,23 = 0,77)
σ = 300 ml.
μ = 3500 ml.
Graphic Calculator: invNorm(0,23;3500;300) = 3278, 35 ml.
Samantha's lung capacity is 3278,35 ml.
Of course, the same anwser, but for me this is easier :)
(Greetings from the Netherlands and I apologize for my English)