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?

  • $\begingroup$ self-study? If so, add the tag and please read the wiki. $\endgroup$
    – Xi'an
    Apr 11 '15 at 19:38
  • $\begingroup$ Routine bookwork type questions are classified as self-study (and should be tagged as such). The self-study tag wiki can be found here. Please add the tag and modify your question to incorporate the requested information. $\endgroup$
    – Glen_b
    Apr 12 '15 at 2:13

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.


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