Question

A quality control manager for a company that manufactures aluminum water pipes believes that the product lengths of one of the pipes produced can be modeled by a uniform probability distribution over the interval 28.50 to 31.75 feet. Determine the probability that a pipe produced has length greater than 30 feet.

Answer 1

The probability that a pipe produced has length greater than 30 feet is 0.5385.

Explanation:

Let X = product lengths of the pipes produced by a company.

The random variable X is Uniformly distributed with parameters a = 28.50 feet to b = 31.75 feet.

The probability density function of Uniform random variable is:

`f_(X)(x)=\left \{ {{(1)/(b-a);\ a<X<b,\ a<b} \atop {0;\ otherwise}} \right.`

Compute the probability that a pipe produced has length greater than 30 feet as follows:

`P (X>30)=\int\limits^(31.75)_(30) {(1)/(31.75-28.50)} \, dx \\`

`=(1)/(3.25)* \int\limits^(31.75)_(30) {1} \, dx \\`

`=(1)/(3.25)* [31.75-30]`

`=0.538462\\\approx0.5385`

Thus, the probability that a pipe produced has length greater than 30 feet is 0.5385.