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Kamila [148]
3 years ago
13

Assume that trees are subjected to different levels of carbon dioxide atmosphere with 8% of the trees in a minimal growth condit

ion at 350 parts per million (ppm), 11% at 440 ppm (slow growth), 48% at 560 ppm (moderate growth), and 33% at 640 ppm (rapid growth). What is the mean and standard deviation of the carbon dioxide atmosphere (in ppm) for these trees? The mean is ppm. [Round your answer to one decimal place (e.g. 98.7).] The standard deviation is ppm. [Round your answer to two decimal places (e.g. 98.76).]
Mathematics
1 answer:
Daniel [21]3 years ago
7 0

Answer: The mean is <u>556.4</u> ppm.

The standard deviation is<u> 84.92</u> ppm.

Step-by-step explanation:

Let X denotes the concentration of carbon (ppm) .

Given :  

X             p(x)

350        0.08

440        0.11

560        0.48

640         0.33

The mean(expected value)  is given by :-

E[x]=\sum x p(x)

\Rightarrow\ E[x]=(350)(0.08)+(440)(0.11)+(560)(0.48)+(640)(0.33)=556.4

Hence, the mean is <u>556.4</u> ppm.

Now, E[x^2]=\sum x^2 p(x)

\Rightarrow\ E[x]=(350)^2(0.08)+(440)^2(0.11)+(560)^2(0.48)+(640)^2(0.33)=316792

\text{Var(x)}=E[x^2]-[E[x]]^2\\\\=316792-556.4^2\\\\=316792-309580.96=7211.04

Standard deviation: \sigma=\sqrt{7211.04}=84.9178426481\approx84.92

Hence, The standard deviation is<u> 84.92</u> ppm.

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