# Obscure Probability Question

Suppose that blood chloride concentration (mmol/L) has a normal distribution with mean 104 and standard deviation 5 (information in the article “Mathematical Model of Chloride Concentration in Human Blood,” J. of Med. Engr. and Tech., 2006: 25–30, including a normal probability plot as described in Section 4.6, supports this assumption).

a.What is the probability that chloride concentration equals 105? Is less than 105? Is at most 105?

b.What is the probability that chloride concentration differs from the mean by more than 1 standard deviation? Does this probability depend on the values of $\sigma$ and $\mu$

c. How would you characterize the most extreme .1% of chloride concentration values?

I am having trouble with part c). I'm just not quite sure what it is asking.

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I guess you should find out the range of the lowest $0.05\%$ of all values, and similarily the range of the highest $0.05\%$ of all the values. The first range will have the form $(-\infty,a)$, and the second range will have the form $(b,\infty)$.
Do you possibly mean $.05$\%? Are there an infinite amount of intervals? –  Mack Mar 10 '13 at 19:56
There are indeed infinitely many pairs $(-b,a)$ such that $\Pr(Z\gt a)+\Pr(Z\lt -b)=0.001$. However, if we choose symmetric pairs $(-a,a)$ then there is only one value of $a$ that works. I have not done a detailed calculation, the cdf moves slowly around there. Something like $a=3.3$ works. –  André Nicolas Mar 10 '13 at 20:25