Question

Page 5 Name (please print) V. Suppose that X follows a lognormal distribution with $\mu = E(ln(X)) = 3.5$ and $\sigma = \sqrt{V(ln(X))} = .6$. (5) a) What are the mean and standard deviation of X? b) What is the probability that X exceeds 95? c) What is the probabiltiy that X is at least 150? Greater than 150?

          Page 5
Name (please print)
V.
Suppose that X follows a lognormal distribution with $\mu = E(ln(X)) = 3.5$ and $\sigma = \sqrt{V(ln(X))} = .6$.
(5)
a) What are the mean and standard deviation of X?
b) What is the probability that X exceeds 95?
c) What is the probabiltiy that X is at least 150? Greater than 150?

Page 5
Name (please print)
V.
Suppose that X follows a lognormal distribution with μ = E(ln(X)) = 3.5 and σ = √(V(ln(X))) = .6.
(5)
a) What are the mean and standard deviation of X?
b) What is the probability that X exceeds 95?
c) What is the probabiltiy that X is at least 150? Greater than 150?

Added by Kristin W.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Christopher Dzorkpata

02/26/2022

Step 1

Step 1: The mean and standard deviation of a lognormal distribution are given by: $$E(X) = exp(\mu + \frac{\sigma^2}{2})$$ $$SD(X) = \sqrt{exp(2\mu + \sigma^2)(exp(\sigma^2) - 1)}$$ Show more…

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Page 5 Name (please print) V. Suppose that X follows a lognormal distribution with µ = E(ln(X)) = 3.5 and r = √V(ln(X)) = .6. (5) a) What are the mean and standard deviation of X? b) What is the probability that X exceeds 95? c) What is the probabiltiy that X is at least 150? Greater than 150?