Question

3.assume the random variable x is normally distributed with mean (wierd character)..(u)=90 and standard deviation o=4 find the indicated probability P(78<x<88) (round="" to="" four="" decimal="" places="" as="" needed)

Answer 1

3. assume the random variable $x$ is normally distributed with mean (wierd character).(u)=90 and standard deviation $\sigma = 4$ find the indicated probability

P(78<x<88) (round="" to="" decimal="" places" as="" needed) please show your work

$$\mathrm{P}(78 < \mathrm{x} < 88) = \mathrm{P}\left(\frac{78 - 90}{4} < \frac{\mathrm{x} - 90}{4} < \frac{88 - 90}{4}\right) = \mathrm{P}\left(-3 < \frac{\mathrm{x} - 90}{4} < 0.5\right) = \text{by CLT (Central Limit Theorem)} =$$ $$\begin{array}{l} \mathrm{F}(-0.5) - \mathrm{F}(-3) = \mathrm{F}(3) - \mathrm{F}(0.5) = 0.9986 - 0.6915 \\ = 0.3071 \\ \end{array}$$