Given 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.
(A) less than 11 pounds
Since weight loss is spread evenly over the range of 6 to 12 pounds.
The average weight loss is \(\frac{(6+12)}{2} \) = 9 pounds.
The width of range is 11 - 6 = 5 pounds
The height of curve is \(\frac1{(12-6) } = \frac16\)
which reciprocal of width.
The area of triangle formed by width and height is \(5(\frac16) = \frac56\)
Therefore, probability of losing less than 11 pounds is \(\frac 56\).
(B) Between 8.5 pounds and 10 pounds
Width of range is 10 - 8.5 = 1.5 pounds
Height of curve is \(\frac1{(12-6) } = \frac16\)
which is reciprocal of width.
Since height loss is spread evenly the area of triangle formed by width and height is \(1.5(\frac16) = \frac14\)
Therefore, the probability of losing between 8.5 to 10 ponds is \(\frac14\).
