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