Question

according to a study by dr. john mcdougall of his live - in weight loss program at st. helena hospital, the people who follow his program lose between six and 15 pounds a month until they approach trim body weight. lets suppose that the weight loss is uniformly distributed. we are interested in the weight loss of a randomly selected individual following the program for one month. find the probability that the individual lost more than ten pounds in a month. a. 10.5 b. 26 c. $\frac{5}{9}$

Explanation:

Step1: Identify distribution parameters

For a uniform distribution on the interval $[a,b]$, here $a = 6$ and $b=15$.

Step2: Use probability formula for uniform distribution

The probability density function of a uniform distribution $U(a,b)$ is $f(x)=\frac{1}{b - a}$ for $a\leq x\leq b$, and the probability $P(X>x)=\frac{b - x}{b - a}$. We want $P(X > 10)$, so we substitute $x = 10$, $a = 6$, and $b = 15$ into the formula.
\[P(X>10)=\frac{15 - 10}{15 - 6}=\frac{5}{9}\]

Answer:

c. $\frac{5}{9}$