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...

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.

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thilina-g's profile pic

thilina-g | College Teacher | (Level 1) Educator

Posted on

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).

Therefore,

`-0.74 = (x-3500)/300`

`x-3500 = -222`

`x = 3500-222`

`x = 3278 ml.`

 

Therefore Samantha's lung capacity is 3278 ml.

Sources:
irislirisl's profile pic

irislirisl | Student, Grade 11 | (Level 1) Honors

Posted on

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)

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