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. a. Find the mean and standard deviation of the thickness of the protective coating. b. Find also the probability that the coating is less than 35 microns thick

a) For this case the mean is given by:

The variance is given by:

And the deviation would be:

b) For this case we want to find this probability:

And we can use the cumulative distribution function given by:

And using this we got:

Step-by-step explanation:

For this case we define the random variable X as the hickness of a protective coating applied to a conductor and we know that the distribution of X is given by:

Part a

For this case the mean is given by:

The variance is given by:

And the deviation would be:

Part b

For this case we want to find this probability:

And we can use the cumulative distribution function given by:

And using this we got:

step-by-step explanation:

the multiplicative inverse of a fraction a/b is b/a. for the multiplicative inverse of a real number, divide 1 by the number. for example, the reciprocal of 5 is one fifth 1/5 or 0.2, and the reciprocal of 0.25 is 1 divided by 0.25, or 4.