Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. It only takes a minute to sign up.
Sign up to join this community
In a large group of patients, cholesterol level approximates a normal distribution N(μ, σ). Observed that 20% of the members of this group have a cholesterol level of less than 117.7mg/100ml and 8% had levels above 239mg/100ml.
What is the average, μ, of the normal distribution?
Assuming this is a self-study question, here is a hint: $(\mu,\sigma)$ is determined by the system of two equations $$\begin{cases} \Phi(\sigma^{-1}\{117.7-\mu\})=0.2 & \\ \Phi(\sigma^{-1}\{239-\mu\})=0.92 & \end{cases}$$ From there, you can proceed by identifying the $0.2$ and $0.92$ quantiles of the $\mathcal{N}(0,1)$ distribution, concluding by solving a system of two linear equations.
self-study(and should be tagged as such). Theself-studytag wiki can be found here. Please add the tag and modify your question to incorporate the requested information. $\endgroup$