Question

The time it takes to manufacture a product is modeled by a continuous distribution. The time to manufacture one unit can take anywhere from 5 to 6 minutes with equal probability. What distribution can be used to model the random variable, production time

Answer 1

The distribution of the time it takes to manufacture the products can be explained by the continuous Uniform distribution.

Explanation:

An Uniform distribution is the probability distribution of outcomes that are equally likely, i.e. all the outcomes has the same probability of occurrence.

Uniform distribution are discrete and continuous.

A discrete uniform distribution describes the probability distribution of discrete random variable that assumes discrete values. For example, roll of a die.

A continuous uniform distribution describes probability distribution of continuous random variable that assumes values in a specified interval. For example, time it takes to reach school from home.

In this case let the random variable X be defined as the time it takes to manufacture a product.

To manufacture 1 unit the time taken is between 5 to 6 minutes.

Every value in the interval 5 - 6 has equal probability.

The distribution of the time it takes to manufacture the products can be explained by the continuous Uniform distribution.

The probability density function of a continuous Uniform distribution is:

`f(x)=\left \{ {{(1)/(b-a);\ x\ \epsilon\ [a, b]} \atop {0;\ otherwise}} \right.`