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.
-More than 10 pounds
A) $\frac { 2 } { 3 }$
B) $\frac { 1 } { 3 }$
C) $\frac { 1 } { 7 }$
D) $\frac { 5 } { 6 }$

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.
-More than 10 pounds 
A) $\frac { 2 } { 3 }$
B) $\frac { 1 } { 3 }$
C) $\frac { 1 } { 7 }$
D) $\frac { 5 } { 6 }$

Quizplus · Accepted Answer

The range of pounds lost is from 6 to 12, and since the distribution is uniform, the probability of losing more than 10 pounds is the ratio of the length of the interval from 10 to 12 to the length of the entire interval from 6 to 12.

Length of interval from 10 to 12: 12 - 10 = 2
Length of entire interval from 6 to 12: 12 - 6 = 6

Probability of losing more than 10 pounds: 
Probability = (length of interval from 10 to 12) / (length of entire interval from 6 to 12) 
Probability = 2/6 
Probability = 1/3

Therefore, the probability of losing more than 10 pounds is 1/3, which corresponds to choice B.

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