Question

The lengths of a runner's workout have a continuous uniform distribution between 49.29 min and

55.55 min. If one such workout is randomly selected, find P57

Answer 1

Given:

The lengths of a runner's workout have a continuous uniform distribution between 49.29 min and 55.55 min.

To find:

P57

When one workout is randomly selected.

Step-by-step explanation:

Let a =49.29 and b = 55.55

x -uniform (49.29,55.55)

We know that:

`f(x) = (1)/(b - a)`

Replace a =49.29 and b = 55.55 in the above equation.

`f(z) = (1)/(55.55 - 49.29) = (1)/(6.26)`

Let k be the 57th percentile.

P(x < k) = k × f(x)

Replace P(x<k) =0.57 and f(x)=1/6.26 in the above formula.

`0.57 = (k)/(6.26)`

Multiply both sides by 6.26

`0.57 * 6.26 = (k)/(6.26) * 6.26`

`3.5682 = k`

Final answer:

P57 = 3.5682