Independent solution

How to solve this Uniform Distribution question

Setup

Setup

For a continuous uniform variable on an interval with endpoints l and u, write its r-quantile as a linear interpolation between the endpoints.

Q(r)=l+r(u−l),0<r<1Q(r)=l+r(u-l),\qquad 0<r<1

Model

Model

The first supplied interval therefore has a 40th percentile of 51. Set that value equal to the 20th percentile from the interval containing the unknown endpoint x.

25+0.40(90−25)=5125+0.40(90-25)=51
45+0.20(x−45)=5145+0.20(x-45)=51

Compute

Compute

Solve for x, substitute it into the final interval, and take that interval's midpoint.

0.20(x−45)=6⟹x=750.20(x-45)=6\quad\Longrightarrow\quad x=75
[10,x3]=[10,25]\left[10,\frac{x}{3}\right]=[10,25]
Q(0.50)=10+0.50(25−10)=17.5Q(0.50)=10+0.50(25-10)=17.5

Answer

Answer

The requested median is 17.5.

17.5(B)\boxed{17.5\quad\text{(B)}}