Question

The ability of unsaturated field soils to retain water is critical to the soils field capacity. A team of engineers investigated the water retention properties of soil cores comprising silt loam. At a given pressure the water content of the soil was determined to be approximately normally distributed with mean 0.27 and standard deviation 0.04.

i. What is the probability that the water content is less than 0.30?


ii. What is the probability that the water content is between 0.23 and 0.28?


iii. Find the range of water content that will lie in the upper 10%


iv. Find the range of water content that will lie in the middle 95%

Answer 1

i)  the probability that the water content is less than 0.30

x~N(0.27,0.04)

p(x <= 0.30 ) =0.7734

ii)the probability that the water content is between 0.23 and 0.28

x~N(0.27,0.04)

p(0.23 <= x <= 0.28) =0.4401

iii)  the range of water content that will lie in the upper 10%

For example, 10 percent means “10 out of 100,” so this translates to 1/10, and this fraction is equal to 0.1 (just divide 1 by 10 to find this). If you want to work out 10 percent of any number, divide the number by 10.

iv) the range of water content that will lie in the middle 95%

The rule tells us that the middle 95% fall within 2 standard deviations from the mean, so the middle 95% of all scores lie between 60 and 160.