Hi An,
You didn't provide us with a value of μ or σ, so I'll just leave it as μ and σ in the answer:
1. Since x is less than μ we have a negative z score. The z score which corresponds to a probability of 0.4525 between x and μ is 1.67 (you can find this using a table, or using the excel function "=NORMINV(0.5  0.4525, 0, 1)", which computes the z score
for an area of 0.4525 between x and μ).
Therefore the desired value of x is:
x = μ  1.67σ
or if μ = 0 and σ = 1,
x = 1.67
2. I'll leave this one up to you, but its the same as (1), except that you're adding the area to 0.5 in the inverse normal function instead of subtracting it, which will give you a positive z score.
Nov 12

John L.
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