The College Board reported the following mean scores for the three parts of the

Question

The College Board reported the following mean scores for the three parts of the Scholastic Aptitude Test (SAT (The World Almanac, 2009): Critical Reading Mathematics Writing 502 515 494 Assume that the population standard deviation on each part of the test is ?-100. a. What is the probability a sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 502 on the Critical Reading part of the test (to 4 decimals)? 0.66 Round z value in intermediate calculation to 2 decimals places. b. What is the probability a sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 515 on the Mathematics part of the test (to 4 decimals)? 0.66 Round z value in intermediate calculation to 2 decimals places. What is the probability a sample of 100 test takers will provide a sample mean test score within 10 points of the population mean of 494 on the writing part of the test (to 4 decimals)? 0.69 Round z value in intermediate calculation to 2 decimals places. ide Feedback

Explanation / Answer

(a) P(492 < x-bar < 512) [since within 10 points So 502+10=512 and 502-10=492]

(1) z = (492-502)/100/?90

z = -0.9487

(2) z = (512-502)/100/?90

z = 0.9487

P(-0.95< z < 0.95) = 0.6572268

(b). P(505 < x-bar < 525)

1. z = (505-515)/100/ ?90

z = -0.95

2. z = (525-515)/100/ ?90

z = 0.95

P(-0.95< z < 0.95) = 0.6572268


c. P(484 < x-bar < 504)

1. z = (484-494)/100/?100

z = -1 is 0.1587

2. z = (504-494)/100/?100

z = 1 is 0.8413

So P(-1< z <1) = 0.6827

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