# 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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### 2 Answers

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.**

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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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