Question

The water content of soil from a borrow site is normally distributed with a mean of 14% and a standard deviation of 2.5%. What is the probability that a sample taken from the site will have a water content above 16% or below 12%?

Answer 1

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:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

P(water content above 16% or below 12%)

= 1 - P(water content between 12% and 16%)

$=1 - P(12 \leq x \leq 16) =1 - P(\displaystyle\frac{12 - 14}{2.5} \leq z \leq \displaystyle\frac{16-14}{2.5})\\\\=1 - (P(-0.8 \leq z \leq 0.8))\\\\=1 -(P(z \leq 0.8) - P(z < -0.8))\\=1-( 0.788 -0.212) = 0.424 = 42.4\%$

0.424 is the probability that a sample taken from the site will have a water content above 16% or below 12%.