SOLUTION: X has a normal distribution with a mean of 75.0 and a standard deviation of 2.5. Find the following probabilities: a) P(x < 70.0) i did 70-75/2.5= -2 but dont know what's next

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Question 186305: X has a normal distribution with a mean of 75.0 and a standard deviation of 2.5. Find the following probabilities:
a) P(x < 70.0) i did 70-75/2.5= -2 but dont know what's next
b) P(72.5 < x < 80.0) not sure
c) P(x >82.5) 75-82.5/2.5= -3 i use table to look for z
3=0.3821 p(z<-3)=0.3821

Answer by stanbon(57282) About Me  (Show Source):
You can put this solution on YOUR website!
X has a normal distribution with a mean of 75.0 and a standard deviation of 2.5. Find the following probabilities:
-----------------------
a) P(x < 70.0) i did (70-75)/2.5= -2 but dont know what's next
P(x < 70) = P(z < -2) = 0.0228
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b) P(72.5 < x < 80.0) not sure
z(72.5) = (72.5-75)/2.5 = -2.5/2.5 = -1
z(80) = (80-75)/2.5 = 2
P(72.5 < x < 80) = P(-1 < z < 2) = 0.8186
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c) P(x >82.5)
z(82.5) = (82.5-75)/2.5 = 3
P(x > 82.5) = P(z > 3) = 0.0013


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Cheers,
Stan H.