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 6 and 15 pounds a month until they approach trim body weight. Let's 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. Give the distribution of X. Enter an exact number as an integer, fraction, or decimal.f(x)=__ where ≤ X ≤. mu = sigma =. Find the probability that the individual lost more than 8 pounds in a month.Suppose it is known that the individual lost more than 9 pounds in a month. Find the probability that he lost less than 13 pounds in the month.

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 6 and 15 pounds a month until they approach trim body weight. Let's 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. Give the distribution of X. Enter an exact number as an integer, fraction, or decimal.f(x)=__ where ≤ X ≤. mu = sigma =. Find the probability that the individual lost more than 8 pounds in a month.Suppose it is known that the individual lost more than 9 pounds in a month. Find the probability that he lost less than 13 pounds in the month.

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asked 2020-12-01
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 6 and 15 pounds a month until they approach trim body weight. Let's 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. Give the distribution of X. Enter an exact number as an integer, fraction, or decimal.\(\displaystyle{f{{\left({x}\right)}}}=_{_}\) where \(\displaystyle≤{X}≤.\mu=\sigma=\). Find the probability that the individual lost more than 8 pounds in a month.Suppose it is known that the individual lost more than 9 pounds in a month. Find the probability that he lost less than 13 pounds in the month.

Answers (1)

2020-12-02
Step 1 Given, 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 6 and 15 pounds a month until they approach trim body weight. Let's suppose that the weight loss is uniformly distributed. Step 2 The random variable \(\displaystyle{X}=\) Weight loss in pounds Given \(\displaystyle{a}={6},{b}={15}\)
\(\displaystyle{X}\sim{U}{\left({a},{b}\right)}\Rightarrow{X}\sim{U}{\left({6},{15}\right)}\)
\(\displaystyle{f{{\left({x}\right)}}}=\frac{{1}}{{{b}-{a}}}\)
\(\displaystyle=\frac{{1}}{{{15}-{6}}}\)
\(\displaystyle=\frac{{1}}{{9}}\)
\(\displaystyle\mu=\frac{{{a}+{b}}}{{2}}\)
\(\displaystyle={\left({6}+\frac{{15}}{{2}}\right.}\)
\(\displaystyle=\frac{{21}}{{2}}\)
\(\displaystyle={10.5}\)
\(\displaystyle\sigma=\frac{{{b}-{a}}}{\sqrt{{{12}}}}\)
\(\displaystyle=\frac{{{15}-{6}}}{\sqrt{{{12}}}}\)
\(\displaystyle=\frac{{9}}{\sqrt{{{12}}}}\)
\(\displaystyle={2.5980}\) Step 3 The probability that the individual lost more than 8 pounds in a month: \(\displaystyle{P}{\left({x}{>}{8}\right)}=\frac{{{b}-{x}}}{{{b}-{a}}}\)
\(\displaystyle=\frac{{{15}-{8}}}{{{15}-{6}}}\)
\(\displaystyle={0.7778}\) (rounded off to 4 decimals) Step 4 Suppose it is known that the individual lost more than 9 pounds in a month. The probability that he lost less than 13 pounds in the month: \(\displaystyle{P}{\left({x}{<}{13}{m}{i}{d}{x}{>}{9}\right)}={P}\frac{{{9}{<}{x}{<}{13}}}{{P}}{\left({x}{>}{9}\right)}\)
\(\displaystyle{\frac{{{x}_{{{2}}}-{x}_{{{1}}}}}{{{b}-{a}}}}\ {\frac{{{b}-{x}}}{{{b}-{a}}}}\)
\(\displaystyle=\frac{{\frac{{{13}-{9}}}{{{15}-{6}}}}}{{\frac{{{15}-{9}}}{{{15}-{6}}}}}\)
\(\displaystyle=\frac{{\frac{{4}}{{9}}}}{{\frac{{6}}{{9}}}}\)
\(\displaystyle=\frac{{2}}{{3}}\)
\(\displaystyle={0.6667}\) (rounded off to 4 decimals)
0

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