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

Answer:

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

And replacing we got:

$P(24< X<38)=\frac{38-20}{40-20}-\frac{24-20}{40-20}= 0.9-0.2= 0.7$

Step-by-step 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:

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

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:

$P(24< X<38)=\frac{38-20}{40-20}-\frac{24-20}{40-20}= 0.9-0.2= 0.7$