Sunday, 25 August 2013

probability in normal density function

probability in normal density function

Q: let X be a continuous random variable with NORMAL DENSITY
$$f(x;\mu,\sigma) = \frac{1}{\sigma\sqrt{2\pi}}e^{−(x−\mu)^2/
2\sigma^2}$$
We know that $\mu = 70$ and $\sigma = 2$.
Find $P(68 \leq X \leq 74)$ and $P(X \geq 73)$:
my approach is ...
Since above is normal distribution..
$$ P\left(\dfrac{a-ì}{ó} \leq Z \leq \dfrac{b-ì}{ó}\right) = P(1 \leq Z
\leq 2) = P(Z\leq2) - P(Z\leq1) $$
but this was wrong because the density function is not standard
distribution so I could not use the table. How can I solve this ?

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