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. less than 99 pounds

Answer 1

Answer: 0.5

Step-by-step explanation:

The probability density function for x that uniformly distributed in interval [a,b] :

$f(x)=\dfrac{1}{b-a}$

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 = $f(x)=\dfrac{1}{12-6}=\dfrac{1}{6}$

Now , the probability of the given range of pounds lost is less than 9 pounds :

$=\int^{12}_{9}\ f(x)\ dx\\\\= \int^{12}_{9}\ \dfrac{1}{6}\ dx\\\\= \dfrac{1}{6}[x]^{12}_{9}\\\\=\dfrac{1}{6}(12-9)=0.5$

Hence, the required probability = 0.5

Answer 2

If the distribution is uniform between 6 and 12, the probability of being less than 99 is 1 (certainty).

_____

Perhaps you intend to find the probability that the loss is less than 9 pounds. That value is

... (9 - 6)/(12 - 6) = 3/6 = 1/2