A normal random variable x has an unknown mean (mu), and a standard deviation of 2.If the probability that x exceeds 7.5 is 0.8023, find the mean(mu).

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A normal random variable `x` has an unknown mean `mu` , and a standard deviation `sigma=2` . If the probability that `x` exceeds 7.5 is 0.8023, find the mean `mu` .

(1) Recall that we convert the value of a random variable to a `z` score by the formula `z=(x-mu)/sigma`...

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A normal random variable `x` has an unknown mean `mu` , and a standard deviation `sigma=2` . If the probability that `x` exceeds 7.5 is 0.8023, find the mean `mu` .

(1) Recall that we convert the value of a random variable to a `z` score by the formula `z=(x-mu)/sigma` .

(2) If the probability that `x` exceeds 7.5 is 0.8023, then the probability that `x` is less than 7.5 is 0.1977; we can get the corresponding `z` score for .1977 from a table or utility to be `z~~-.8499` .

(3) Substitute the known quantities and solve for `mu` :

`-.8499 = (7.5-mu)/2` or `mu~~9.1997`

Thus we can say that the mean is approximately 9.2

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