Given X~N( x̄, σ2), P(X > 80) = 0.1, P(X < 72) = 0.2, find x̄ and σ2 .

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Given X~N( x̄, σ2), P(X > 80) = 0.1, P(X < 72) = 0.2, find x̄ and σ2 .
Expert Solution
Step 1: Determine the given ifnromation

For the distribution of the variable X, it is given that the distribution is normal with parameters as follows:

The mean, X¯ and the variance σ2 (i.e., standard deviation, σ).

For a random raw score, X, the specified probabilities are as follows:

P(X>80)=0.1 and P(X<72)=0.2


The z-score for a random raw score, X is:

z=XX¯σ





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