The thickness x 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 less than 36 microns thick? Provide the answer as a fraction to one decimal place.

Question

The thickness x 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 less than 36 microns thick? Provide the answer as a fraction to one decimal place.

BlackTom AI · Accepted Answer

We start by identifying the distribution and the interval: the coating thickness x is uniformly distributed on [20, 40] microns. 
Since it’s a uniform distribution, the probability that x falls between 20 and some value a (within the interval) is proportional to the length of that subinterval relative to the total interval length. 
Total interval length = 40 − 20 = 20 microns. 
We want P(x < 36) which corresponds to the subinterval [20, 36]. Length of this subinterval = 36 − 20 = 16 microns. 
Thus, P(x < 36) = length of [20,36] / length of [20,40] = 16 / 20 = 0.8. 
Expressing the result as requested: this probability is 0.8 (which is 0.8 when written with one decimal place). 
Note the key idea: for a uniform distribution, probabilities map directly to relative lengths of subintervals within the support, so greater subinterval length yields higher probability until you reach the end point of the interval.

The thickness x 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 less than 36 microns thick? Provide the answer as a fraction to one decimal place.

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