Question

The thickness of a protective coating applied to a conductor designed to work in corrosive conditions follows a uniform distribution over the interval [20;40] microns. Find the probability that the coating is between 24 and 38.

Answer 1

`P(24< X<38)= P(X<38) -P(X<24)= F(38) -F(24)`

And replacing we got:

`P(24< X<38)=(38-20)/(40-20)-(24-20)/(40-20)= 0.9-0.2= 0.7`

Explanation:

We can define the random variable X as the thickness of a protective coating applied to a conductor designed to work in corrosive conditions. And the distribution for X is given by:

`X \sim Unif (a = 20, b=40)`

And we want to find this probability:

`P(24< X<38)`

And in order to find this probability we can use the cumulative distribution function given by:

`F(x) = (x-a)/(b-a) , a\leq X \leq b`

And if we use this formula for the probability desired we have:

`P(24< X<38)= P(X<38) -P(X<24)= F(38) -F(24)`

And replacing we got:

`P(24< X<38)=(38-20)/(40-20)-(24-20)/(40-20)= 0.9-0.2= 0.7`