SOLUTION: Given a normal distribution with  = 100 and  = 10, what is the probability that: a. X > 80? b. X < 65? c. X < 75 or X > 90? d. Between what two X values (symmetrically

Question 1167595: Given a normal distribution with  = 100 and  = 10, what is the probability that:
a. X > 80?
b. X < 65?
c. X < 75 or X > 90?
d. Between what two X values (symmetrically distributed around the mean) are ninety percent of the values?

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
z=(x-mean)/sd
a. z is >-2 and that has probability 0.9772
b. z<-3.6 and that probability is 0.00016
c. x< 75 and x>90 is z<-2.5 and z >-1
that probability is 0.0062 and 0.8413 or sum 0.8475
90% of the values are between z=-1.645 and +1.645 or between 83.55 and 116.45
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