Question

A publication released the results of a study of the evolution of a certain mineral in the​ Earth's crust. Researchers estimate that the trace amount of this mineral x in reservoirs follows a uniform distribution ranging between 55 and 1010 parts per million
a. Find E(x) and interpret its value
b. Compute P(2.875 x35)
c. Computn Plx<4.125)

Answer 1

Answer:

a) $E(A)=\frac{1+6}{2}=3.5 ppm$

b) $P(2.875$

c) $P(X$

Step-by-step explanation:

If we work with the limits defined from 5 to 10 then part b and c from this question not makes sense. If we work with the limits 1 and 6 all the parts for the question makes sense because if we work with 5 and 10 the only thing that we can find is the expected value $E(A) = \frac{5+10}{2}= 7.5$

Assuming the following correct question : "A publication released the results of a study of the evolution of a certain mineral in the​ Earth's crust. Researchers estimate that the trace amount of this mineral x in reservoirs follows a uniform distribution ranging between 1 and 6 parts per million"

Solution to the problem

Let A the random variable that represent " amount of the mineral x ". And we know that the distribution of A is given by:

$A\sim Uniform(1 ,6)$

Part a

For this uniform distribution the expected value is given by $E(X) =\frac{a+b}{2}$ where X is the random variable, and a,b represent the limits for the distribution. If we apply this for our case we got:

$E(A)=\frac{1+6}{2}=3.5 ppm$

Part b

For this case we can use the cumulative distribution function for the uniform distribution given by:

$F(X=x)= \frac{x-a}{b-a} = \frac{x}{6-1} =\frac{x-1}{5} , 1 \leq X \leq 6$

And we want this probability:$P(2.875$Part c

For this case we want this probability:

$P(X$