Question

4. A simple random sample of size n = 36 is obtained from a population with u = 70 and o = 24. (a) Describe the sampling distribution of x. (b) What is P (X>76) ? (c) What is P (x561.4)? (d) What is P (68 <x< 77.6) ?

Answer 1

solution Given that l= 70 o= 24 n = 36 M = x - to 67 o tac Sampling Distribution of the sample mean Ť is the symbol used to represent the Sample mean. The central limit theorem States that if a large enough sample is taken (n>30) then the sampling distribution of x is approximately a normel distal buion with a mean of it and a standard deulation of on. b) P(X>76) = IP (8 (76) - 1-P/x-ux ( 76-70 ) - 1-P (2 21.5) - 1-0.9332 0.0668 Lp (X>76) = 0.0668)

c) P ( X < 61.4) = P(x-ux (614-70) P (z 4 - 2-15) P(xs 6114) - 0.0158 0.0158 d) P (68<x< 17-6)=P(68-70 < x-ux 241.6-70 P(-0.5<2L 1.9) = P( 221.g) - P( ZL-05) = = 0.9713 - 0.3085 0 - 6628 IP (68 < X < 77.6) = 0.6628