Assume that the weight loss for the first month of a diet program varies between 6 pounds and 12 pounds, and is spread evenly over the range of possibilities, so that there is a uniform distribution. Find the probability of the given range of pounds lost.
-Between 8.5 pounds and 10 pounds
A) $\frac { 3 } { 4 }$
B) $\frac { 1 } { 2 }$
C) $\frac { 1 } { 4 }$
D) $\frac { 1 } { 3 }$

Question

Assume that the weight loss for the first month of a diet program varies between 6 pounds and 12 pounds, and is spread evenly over the range of possibilities, so that there is a uniform distribution. Find the probability of the given range of pounds lost.
-Between 8.5 pounds and 10 pounds 
A) $\frac { 3 } { 4 }$
B) $\frac { 1 } { 2 }$
C) $\frac { 1 } { 4 }$
D) $\frac { 1 } { 3 }$

Quizplus · Accepted Answer

The total range of pounds lost is 12 - 6 = 6 pounds. The middle of this range is (12 + 6) / 2 = 9 pounds. 
To find the probability of losing between 8.5 pounds and 10 pounds, we need to find the portion of the total range that corresponds to this interval. 
The difference between 8.5 pounds and 9 pounds is 0.5 pounds, which is 1/12 of the total range. 
The difference between 10 pounds and 9 pounds is also 1/12 of the total range. 
Therefore, the probability of losing between 8.5 pounds and 10 pounds is (1/12) + (1/12) = 1/6, which simplifies to 1/4 or 0.25.

Assume That the Weight Loss for the First Month of a Diet