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

Answer:

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

Step-by-step 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:

$f_{X}(x)=\left \{ {{\frac{1}{b-a};\ a$

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

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

                 $=\frac{1}{3.25}\times \int\limits^{31.75}_{30} {1} \, dx$

                 $=\frac{1}{3.25}\times [31.75-30]$

                 $=0.538462\\\approx0.5385$

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