Normal distributions--I can't remember how to do this
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Normal distributions--I can't remember how to do this

[From: ] [author: ] [Date: 12-03-02] [Hit: ]
I cant find anything in my book with similar problems, unfortunately.-For X, Im not sure if it is 10.z=(10- 57)/8.5=-5.......
Let X be a normally distributed random variable with mean 57 and standard deviation 8.5. Let Y = 2X + 35. Find P (Y < 170) and P (X > 10).

I can't find anything in my book with similar problems, unfortunately.

-
For X, I'm not sure if it is 10.Anyways change to z-scores and find the probability from the tables

z=(10- 57)/8.5=-5.53

P(X>10)=P(z>-5.53)=1

For Y, the mean is affected by addition and multiplication but standard deviation is affected only by multiplication

mean for Y=2(57)+35=149

SD for Y=2(8.5)=17

z=(170-149)/17=1.24

P(Y<170)=P(z<1.24)=0.8925
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