STA215H5 Lecture Notes - Lecture 3: Standard Deviation, Normal Distribution, Standardized Test
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The -3 shifts the graph 3 units to the right. () the blue bell curve, symmetry about 3 f xx m = = (cid:894)(cid:1007)(cid:895) the (cid:271)eige (cid:271)ell (cid:272)ur(cid:448)e, s(cid:455)(cid:373)(cid:373)etr(cid:455) a(cid:271)out (cid:1004) f (cid:454) (cid:454) (cid:373) = = The (cid:1007) (cid:894)horizo(cid:374)tall(cid:455)(cid:895) stret(cid:272)hes the graph (cid:271)(cid:455) a fa(cid:272)tor of (cid:1007). f x s. 1 ( 3) the blue bell curve (blue and green area), spread 3 1 3 f x s = If we have a sample of x"s from a normal distribution, x ~ n(m, s): their z-scores are a sample of z"s fro(cid:373) the sta(cid:374)dard (cid:374)or(cid:373)al distribution z ~ n(0, 1) We can make z-scores for data from any distribution, but the z- scores are only normal if the original distribution was also normal. Grades on a standardized test have population mean m= 75 and population standard deviation s= 15. Ella"s s(cid:272)ore is (cid:1004). 8 sta(cid:374)dard de(cid:448)iations above the mean. To(cid:374)(cid:455)"s s(cid:272)ore is (cid:1005). (cid:1008) sta(cid:374)dard de(cid:448)iatio(cid:374)s (cid:271)elo(cid:449) the (cid:373)ea(cid:374).
