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Suppose x is normally distributed random variable with μ = 12 and σ =2. Find each of the following probabilities. a. P (x ≥ 13.5) b. P (x ≤ 8) c. P (12.62 ≤ x ≤ 16.54) d. P (7.02 ≤ x ≤ 15.32)

Collaborative Statistics
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They just want you to find Z-scores and look up the probabilities in tables. e.g. for the first, find the area to the right of \(Z\) where $$Z=\frac{13.5-12}2=\frac{1.5}2=0.75$$You can determine the area to the left and subtract from 1.
(b) just wants the area to the left of \(Z=(8-12)/2=-4/2=-2\). Use your table. For (c) and (d), they want the area between two \(Z\):|dw:1370722148193:dw|
Oldrin, I don't have a solid background in Algebra or statistics. So i have problems working these problems out. I would not know how to get these anwers to c. and d. without a step by step.

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The answer they have for a and b are 0.227 and 0.023?
Okay. For (c), first find the appropriate \(Z\) scores:$$Z_1=\frac{12.62-12}2=\frac{0.62}2=0.31\\Z_2=\frac{16.52-12}2=\frac{4.52}2=2.26$$We want the area between the two. Graphically, you can see this is the difference in their respective left-tails:|dw:1370722767214:dw|
So find the areas to the left of \(Z=2.26\) and \(Z=0.31\) in your table. Find their difference.

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