Question

SAT scores have μ=1500 and σ=300. I plan to collect a sample with 900 students. The average of sample means from samples of n=900 is ____ The SD of sample means from samples of n=900 is What are the chances of getting sample mean less than 1500? P(x ̅<1500)=______ First, calculate the z-score. Then use Stata or the Online Stat Book. What are the chances of getting sample mean less than 1480? P(x ̅<1480)=______ What are the chances of getting sample mean less than 1520? P(x ̅<1520)=______ 95% of all sample means are between approximately _____ and _____ points in the SAT. What are the z-scores you need? (So that 95% of all sample means are between z and -z) With each z-score, find the relevant SAT score.

Answer 1

Solution! Given that M = 1500 6= 3oo n= goo MX=1500 6X = - 300 = 10 Vn goo 67= 10 p6 <1 800) =P [ Boya C1500 70.500 C1500 – 15oo 10 ap [z co] 1 = 0.5 , PC <1500) = 0.5

PCX < 1480) =P PE C 14301500) =P [ z < -2] = 0.0 228 PCT < 1480 ) = 0.0228 c) PCX < 1520) =P <152031500 - e8 68 <1520-1500 10 =P [z a 2] = 0.9772 P Q <1520) = 0.9772

- 95 olo dal-95 % 2=1-0.95 X = 0.05 = 0.05 – 0.025 2 1-212= |-0.025 = 0.975 2212= 20.025 = -1.960 Z1-212= 20.975 = +1.960 Using Z-score formula - Xz z 6x tux X = -1.960 X 10 tisoo X=1480.4 X= Z 6x tux X = tl.960 x10 tisoo X- 1519.6 Between 1480 and 1520