## AJACW22 2 years ago 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)

1. oldrin.bataku

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.

2. oldrin.bataku

(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|

3. AJACW22

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.

4. AJACW22

The answer they have for a and b are 0.227 and 0.023?

5. oldrin.bataku

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|

6. oldrin.bataku

So find the areas to the left of $$Z=2.26$$ and $$Z=0.31$$ in your table. Find their difference.