In a normal distribution with mean 3 and variance 49, what are the upper and lower limit scores for the middle 50% of the data?

-how do I find the answer from the z-score table?

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- Oct 27th 2008, 11:23 AM #1

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- Oct 27th 2008, 02:55 PM #2
Let $\displaystyle \Pr(X > x_2) = 0.25$ and $\displaystyle \Pr(X < x_1) = 0.25$. Your task is to find the value of $\displaystyle x_2$ and $\displaystyle x_1$.

$\displaystyle \Pr(Z > z*) = 0.25 \Rightarrow \Pr(Z < z*) = 0.75 \Rightarrow z* = 0.6745$ (using whatever way you've been taught to deal with an inverse normal situation).

Therefore $\displaystyle z* = \frac{x_2 - 3}{7}$. Solve for $\displaystyle x_2$. Use the symmetry of the normal distribution to therefore get $\displaystyle x_1$.