Question

Suppose that the number of pounds of grapes sold by the Smalltown Co-op grocery store in a day is equally likely to be anywhere between 0 and 100 pounds (fractional values are possible). If you use a probability density function to describe the number of pounds of grapes sold daily by the store, the height of the function for any number of pounds between 0 and 100 is

Answer 1

The height of the function for any number of pounds between 0 and 100 is 0.01.

Explanation:

As described, the probability density function is a uniform probability density function, between the values 0 and 100 pounds.

To calculate the height h of the probability density function, we can write:

`\int\limits^(100)_0 {h} \, dx=1`

If we solved this integration and rearrange

`\int\limits^(100)_0 {h} \, dx=1\\h*(100-0)=1\\100*h=1\\h=0.01`

The value of the height of the probability density function is 0.01 for every value between 0 and 100 pounds.