Question

0,25. For rand population, obta Jon distribution of X and Y. Are 8 and Y Hupunuent? 4+2 (b) Ages of 5 persons have me ons have incan recorded as (in years) 14, 19. 17, 25. For random samples of size 3 drawn without replacement from this ulation, obtain the sampling distribution of sample mean (K). Show at the mean of x equals the population mean and obtain the standard 2+2+2 (c) (i) Form a population of large number of men with a standard beviation 5; a sample is drawn and the standard error is found to be 0.3. What is the sample size? (ii) A random sample of size 25 is taken from a e error of x. Nuo°) with u = 30 and o² = 16. Would the probability that the sample mean would lie between 25 and 35 be greater than 0.99? (Giver 2+ hat | (Z)dZ = 0.9973)?

please solve b and c part i)

Answer 1

a 6=5 SE -0.5 64 na? 5x - 6 os = 1 In - 5/5 = 10 n=100

population in {14, 19, 172, 253 Sample mean (u) = 19 312 So 166 18.6 population sample Sample distribuhn { 14, 19, 177 { 19, 17, 20} { 17, 20, 25} & 14, 17, 2} {14, 20, 25} Hence, proved the sample meen od same distribuhon is same I as the population mean. 20.6 19.6 6=1[19-16 6)+ [1918.6] + [26-19] + [ 17-19). 19.3 21.3 17.6 { 14, 19,25% { 19, 20, 25} { 14, 19, 20} 19,2,osb ( 14, 17, 23 6=[3.6+0.4+ 1.6+2+06+2 7+13+14 2e- 376 40% ] 21.3 - 6- 1.78 x Sample&ror 39.3 19.103