The distribution of SAT scores of all college-bound seniors taking the SAT in 2014 was approximately normal with a mean of 14971497 1497 1497 and standard deviation of 322 322 322 322 . Let X=X= X= X, equals the score of a randomly selected tester from this group. Find P(X<1200)P(X<1200) P(X<1200) P, (, X, is less than, 1200, ).

Given Information:

Mean = μ = 1497

Standard deviation = σ = 322

test value = x = 1200

Required Information:

P(x < 1200) = ?

P(x < 1200) = 0.17879

Explanation:

First we will find the z-score

P(x < X) = P(z < (x - μ)/σ)

P(x < 1200) = P(z < (1200 - 1497)/322)

P(x < 1200) = P(z < -0.92)

The z-score corresponding to z < -0.92 from z-table is given by

P(z < -0.92) = 0.17879

Therefore, the probability that SAT the test score will be less than 1200 is 0.17879.

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