Respuesta :
Answer:
0.424 is the probability that a sample taken from the site will have a water content above 16% or below 12%.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 14%
Standard Deviation, σ = 2.5%
We are given that the distribution of water content of soil is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
P(water content above 16% or below 12%)
= 1 - P(water content between 12% and 16%)
[tex]=1 - P(12 \leq x \leq 16) =1 - P(\displaystyle\frac{12 - 14}{2.5} \leq z \leq \displaystyle\frac{16-14}{2.5})\\\\=1 - (P(-0.8 \leq z \leq 0.8))\\\\=1 -(P(z \leq 0.8) - P(z < -0.8))\\=1-( 0.788 -0.212) = 0.424 = 42.4\%[/tex]
0.424 is the probability that a sample taken from the site will have a water content above 16% or below 12%.
