SOLUTION: If X is a normal random variable with standard deviation 3.50, and if the probability that X is more than 10.83 is .1271, then what is the mean of X? Please work out solution so I

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Question 429428: If X is a normal random variable with standard deviation 3.50, and if the probability that X is more than 10.83 is .1271, then what is the mean of X?
Please work out solution so I can see how the answer was achieved.
If X is a normal random variable with a standard deviation 3.50, and if the probability that X is less than 8.83 is .648, then what is the mean of X?

Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
P%28z+=+%28X+-+mu%29%2F3.5+%3E+%2810.83+-+mu%29%2F3.5%29+=+0.1271, or
P%28z+=+%28X+-+mu%29%2F3.5+%3C++%2810.83+-+mu%29%2F3.5%29+=+0.8729
==> %2810.83+-+mu%29%2F3.5+=+1.14, approximately, from a table of standard normal values.
==> 10.83+-+mu+=+3.99
==> mu+=+6.84