The College Board reported the following mean scores for the

The College Board reported the following mean scores for the three parts of the Scholastic Aptitude Test Critical reading 502 Mathematics 515 Writing 494 Assume the population standard deviation on each part of the test is sigma=100. What is the probability a random 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 pari of the test? What is the probability a random 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? Compare this value to that of part a? What is the probability a random sample of 100 test takers will provide a sample mean test score within 10 of the population mean of494 on the writing part of the test?

Solution

(a) P(492 < x-bar < 512)

z = (492-502)/100/90

z = -0.95 is 0.1711

z = (512-502)/100/90

z = 0.95 is 0.8289

(b)   P(505 < x-bar < 525)

z = (505-515)/100/ 90

z = -0.95

z = (525-515)/100/ 90

z = 0.95

P(-0.95< z < 0.95) = 0.6578

P(-0.95< z < 0.95) = 0.6578

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

z = (484-494)/100/100

z = -1 is 0.1587

z = (504-494)/100/100

z = 1 is 0.8413

P(-1< z <1) = 0.6826