Question

76 and o= 18 A simple random sample of size n = 81 is obtained from a population with u (a) Describe the sampling distribution of x. (b) What is P (x> 79.7)? (c) What is P (xs71)? (d) What is P (73.7<x<79.3)? (a) Choose the correct description of the shape of the sampling distribution of x OA. The distribution is skewed right. B. The distribution is approximately normal. OC. The distribution is uniform. OD. The distribution is skewed left OE The shape of the distribution is unknown Find the mean and standard deviation of the sampling distribution of x

Answer 1

We have 612 a By central limit theeremm nas is targe theretove SNOrmal76, 6E 19/Va X 5NOTmal (76, 2) x follows normal clisribulion wth mean u: 16 4 stondarl error 2. 6 consider X- 79.7-76 PiX79.7) p SE 2 = PLZI85) from z-toble 0.032157 Henre PIX79.7 = 0.032 15 7 C) Consider X-4 7/ 76 P SE 2. = P(ZK- 2.5) mey -PIZ 2.5) From z-table -0.0062097 Hente/pxs Ti) = 0.0062097 d) Consider X-4 79.3-76 73.7-76 Pl73.7X 79.3) cp 2 2. - P/-1-15 ZI.65) P(Z-1.15) P(z 65) : PIZ >1.15) - PIZ65 FTom z-hable 1o.12507-0.049g47 O.825459 Hente PI73.7 X 479.3)= 0.825459