Question

Suppose x has a distribution with u = 25 and o = 20. (a) If a random sample of size n = 50 is drawn, find ui, o j and P(25 sxs 27). (Round Oy to two decimal places and the probability to four decimal places.) My = 25 0x = 2.83 P(25 sxs 27) = x (b) If a random sample of size n = 68 is drawn, find us, o x and P(25 sxs 27). (Round og to two decimal places and the probability to four decimal places.) их 0x = P(25 sxs 27) = (c) Why should you expect the probability of part (b) to be higher than that of part (a)? (Hint: Consider the standard deviations in parts (a) and (b).) The standard deviation of part (b) is ---Select--- part (a) because of the ---Select--- v sample size. Therefore, the distribution about ug is ---Select--- V

Answer 1

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Anso Here i M=25 and 5=20 a) Here, n=50 Me=25 oa = 5 =2-83 50 25-25 27-25 S 느 X-M द्र 2.83 2.83 P ( 25+ ā=>) -pe EP (OSZ < 0-7067) = P(Z50.4067)-PC250) P(a5 276 27) 0 2601 Oo 7 bol 0-5 = b) Here, n= 68 20 시지 25 = Ella 2.43 J68 27-25 ñ-M 느 2-43 oa 2-43 Pla5 = 427)=P(25-25 =P(02 OLZ5 0.8230) =P(230.8.230) -P(240) Plas &T=27) = 0.7947 -0.5 0.3947 C) The probability in parl(b) to be hagber. Because as the sample size Snickases, the Standard- deviation will decrease iso the probability in partly be higher than parta) to be