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**MathoMan** X is normally distributed random variable $\displaystyle X\sim(1200,200^2)$ measuring the life span of light bulbs.

You have to determine the value A (number of hours such) that the life span of 95% of light bulbs will last longer than A hours. That means that only 5% of light bulbs will have life span shorter than A and thus such A should be the guaranteed life of light bulbs.

$\displaystyle P(X>A)=0.95$

$\displaystyle 1-P(X<A)=0.95$

$\displaystyle P(X<A)=0.05$

$\displaystyle F_X(A)=0.05$

$\displaystyle \Phi(\frac{A-1200}{200})=0.05$

Now use the table values for standard normal distribution and you'll see that $\displaystyle \Phi(-1.65)\approx 0.05$ so you form the equation

$\displaystyle \frac{A-1200}{200}=-1.65$

$\displaystyle A=870.$