Question

The College Board reported the following mean scores for the three parts of the Scholastic Aptitude Test (SAT) (The World Almanac, 2009) 502 Critical Reading Mathematics Writing 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)? 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)? Round z value in intermediate calculation to 2 decimals places. c. 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)? Round z value in intermediate calculation to 2 decimals places.

Answer 1

In this 10 <Z- P1492<x<512) = pr-Yo population Standard-deviation ca): a:). The probability a sample of no test takers will provide Q Sample mean test score within 10 points of the population means of 502 on the critical Reading part of the test is 4-502 1001190 100/190 PC-0.95< 70-95) - PLZ<0-95]-Plze-0.95] = 0.8289-0:1711 =10.6578 b.) The probability a sample of 96 test takers will provide a samplesmean test score coithin p points of the population mean of 515 on the mathematics part of the test is P(505< X< 525) = P( 505-515 100/10 100|196 P(-0.95<<<0.95) =P[z0.95) -PC24-0-95) 5 6.8289-0.1711 = 10.6578 C) The probability a sample of 100 test takers coill provide a sample mean test score within to points of the population mean of 494 on the writing part of the testis P(484<x<504) =P 484-494 504-494 100/1100 100lió =PL-{<2<l] PLZ«U-PLZC-17 = 0.8413- 0,1587 0.6826 525-515 K Z くまく