The distribution of SAT scores of all college-bound seniors taking the SAT in 2014 was approximately normal with a mean of 14971
497 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, ).
2 answers:
Given Information:
Mean = μ = 1497
Standard deviation = σ = 322
test value = x = 1200
Required Information:
P(x < 1200) = ?
Answer:
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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