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## Homework Statement

Assume X is normally distributed with a mean of 10 and a standard deviation of 2. Determine the value for x that solves P(x < X < 10) = 0.2

## Homework Equations

P(X < x) = P(Z < z) = P(Z < (x - mean)/stdev)

## The Attempt at a Solution

P(X < 10) - P(X < x) = 0.2

P(Z < (10-10)/2) - P(Z < (x-10)/2) = 0.2

P(Z < 0) - P(Z < (x-10)/2) = 0.2

0.5 - P(Z < (x-10)/2) = 0.2

P(Z < (x-10)/2) = 0.3

(x-10)/2 = 0.617911

x - 10 = 1.235822

x = 11.235822

The answer doesn't make sense. x is supposed to be smaller than 10.

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