Question

The body paint, an automobile body paint shop, has determined that the painting time of automobiles is uniformly distributed and that the required time ranges between 45 minutes to 11/2hours.

a. give a mathematical expression for the probability density function.

Answer 1

`f(x) = \left \{ {{(1)/(45), 45 \leq x \leq 90} \atop {0, \text{otherwise}}} \right`

Explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability density function of the uniform distribution is:

`f(x) = \left \{ {{(1)/(b-a), a \leq x \leq b} \atop {0, \text{otherwise}}} \right`

Uniformly distributed and that the required time ranges between 45 minutes to 11/2hours.

Each hour has 60 minutes, so 1 and a half hours is 90 minutes.

So

`a = 45, b = 90`

The probability density function is:

`f(x) = \left \{ {{(1)/(90-45), 45 \leq x \leq 90} \atop {0, \text{otherwise}}} \right`

`f(x) = \left \{ {{(1)/(45), 45 \leq x \leq 90} \atop {0, \text{otherwise}}} \right`

Answer 2

As given, the required time ranges between 45 minutes to 1 1/2hours.

Let the painting time of automobiles be represented by = x

Part a.

give a mathematical expression for the probability density function.

The probability density function is given by =

`f(x)=(1)/(90-45);0`

or we can say it ranges from ,

`45\leq x\leq90`