Question

An article in Health and Population: Perspectives and Issues used lognormal distributionto model blood pressure in humans. The mean systolic blood pressure (SBP) in males age17 120.87 mm Hg. If the co-efficient of variation (100% x standard deviation /mean) is9%, what are the parameter values of the lognormal distribution.A)B)C)D)4.79072.6509-4.79073.6545AnswerСАOBocODSubmit​

Answer 1

Find the parameters of the log-normal distribution

Explanation:

• In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed.
• Thus, if the random variable X is log-normally distributed, then $Y = ln(X)$ has a normal distribution.
• A random variable which is log-normally distributed takes only positive real values.
• here we are the mean as, $\mu=120.87$
• given is the coefficient of variation, hence the standard deviation and variance are given by ,                                  [tex]\sigma=\frac{\mu(CV)}{100}=\frac{120.87(9)}{100} \\ \sigma=10.88(approx.)\ \ \ \ \ \ \ \ \sigma^2=118.34(approx.)[/tex]
• now the probability mass function of this log-normal distribution is ,              $P(X)=\frac{1}{2\sigma\sqrt{2\pi } } e^{-\frac{(ln|X|-\mu)^2}{2\sigma^2} }$                                                                                  here, X- systolic blood pressure(SBP), Mean- $\mu=120.87\ mm\ Hg$   , standard deviation-$\sigma=10.88\ mm\ Hg$ and variance- $\sigma^2=118.34$