A normal random variable x has an unknown mean ? and standard deviation ? = 2.5. If the probability that x exceeds 7.5 is 0.8289, find ?
What will be an ideal response?
It is given that x is normally distributed with ? = 2.5 but with unknown mean ?, and
that P (x > 7.5 ) = 0.8289. In terms of the standard normal random variable z, we can write
P(X > 7.5 ) = P[Z > (7.5 - ?)/2.5] = 0.8289, Z = -0.95
Since the area to the right of (7.5 - ?)/2.5 is greater than 0.5, then (7.5 - ?)/2.5 must be negative, and that P[(7.5 - ?)/2.5 < z < 0] = 0.3289. Hence, (7.5 - ?)/2.5 = -0.095. This implies ? = 9.875.
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