The College Board reported the following mean scores for the Math part of the Scholastic Aptitude Test (SAT) is 515. Assume that the population standard deviation of the test is 100.
What is the probability that a random sample of 64 test takers will provide a sample mean test score between 505 and 520 on the Mathematics part of the test?
Solution :
_{} = / n = 100 / 64 = 12.5
= P[(505 - 515) / 12.5 < ( - _{}) / _{} < (520 - 515) / 12.5)]
= P(-0.8 < Z < 0.4)
= P(Z < 0.4) - P(Z < -0.8)
= 0.4436
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