Central limit theorem

Question

1. An unknown distribution has the following parameters: µx = 45 and σ x = 8 . a sample size of 50 is drawn randomly from the population. Find ΣX where z=-2

Answer 1

I hope I understood this correctly. the Standard deviation of the sample mean should be sigma/sqrt(n) so that will be 8/sqrt(50) . Now if the mean is 45 , that means your z score for the sample mean (the number of standard deviations above the mean) is -2 = (sample mean - mean)/(standard deviation of the sample mean) so -2 = (sample mean-45)/(8/sqrt(50)) . Now you can solve for the sample mean: -2*(8/sqrt(50)) + 45 = sample mean . This was the sample mean of the 50 individuals. The sample mean = the sum/50 . So now all we need is [sample mean]*50 = sum . That's the sum of the Xs that you're looking for