Answer: 0.5
Step-by-step explanation:
The probability density function for x that uniformly distributed in interval [a,b] :
[tex]f(x)=\dfrac{1}{b-a}[/tex]
We 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.
Let x be the weight loss for the first month of a diet program.
Density function = [tex]f(x)=\dfrac{1}{12-6}=\dfrac{1}{6}[/tex]
Now , the probability of the given range of pounds lost is less than 9 pounds :
[tex]=\int^{12}_{9}\ f(x)\ dx\\\\= \int^{12}_{9}\ \dfrac{1}{6}\ dx\\\\= \dfrac{1}{6}[x]^{12}_{9}\\\\=\dfrac{1}{6}(12-9)=0.5[/tex]
Hence, the required probability = 0.5
