Question

1) Suppose a simple random sample of size n=64 is obtained from a population with u = 73 and 6 = 32. (a) Describe the sampling distribution of x. (b) What is P (x>79) ? (c) What is P (563.6) ? (d) What is P (68.6<x<80.2)?

Answer 1

3.0 or ري 6 Bu central limit theorem for sample I sire more sample mean is approximately norma nally dishibuted with mean My= u and In Here l=73 G = 32 = 64 By central limit theorem X X N(73, 324) XN 73 4) .., C b) P ( 7 779 =P ( 27 79.-13 13) 4

EP (271.5) =1-pizeloso from cummulative normal table = 1 - 0.9332 0668 = P ( P ( 2 < 63-6) < 63.6 73 ) = P(Z < 2.35) from cummulative normal table 0.0094 @ P ( 68.6c ñ < 80:2) 13 2. z EPC 68.6 <80:2-73). 4 EP (-101 <zic 4.6) =P ( zs 1.6) - PC z <-1-1) Arom cummulative normal table = + 0.135 1. 9452 8095 .