Question

question 9
0.5 pts
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.
o a 10/5
o b. 2/6
o c 5/9

Explanation:

Step1: Determine the formula for uniform distribution probability

For a uniform distribution \(X\sim U(a,b)\), the probability density function is \(f(x)=\frac{1}{b - a}\) for \(a\leq x\leq b\), and the probability \(P(c<X<d)=\frac{d - c}{b - a}\)

Here, \(a = 6\), \(b=15\), and we want to find \(P(10<X<15)\)

Step2: Substitute values into the formula

Substitute \(a = 6\), \(b = 15\), \(c = 10\), \(d = 15\) into \(P(c<X<d)=\frac{d - c}{b - a}\)

We get \(P(10<X<15)=\frac{15 - 10}{15 - 6}=\frac{5}{9}\approx0.56\)

Wait, maybe there was a mis - read. If we use the formula for continuous uniform distribution \(P(X>x)=\frac{b - x}{b - a}\)

Here \(x = 10\), \(a = 6\), \(b = 15\)

\(P(X>10)=\frac{15-10}{15 - 6}=\frac{5}{9}\)

Answer:

C. \(\frac{5}{9}\)