Question

1.12 points DevoreStat7 5.P 046 The inside diameter of a randomly selected piston ring is a random variable with mean value 11 cm and standard deviation 0.03 cm (a) If X is the sample mean diameter for a random sample of n16 rings, where is the sampling distribution of X centered? cm What is the standard deviation of the X distribution? (Give answer accurate to 3 decimal places) cm (b) Answer the questions posed in part (a) for a sample size of n - 64 rings. Where is the sampling distribution of X centered? What is the standard deviation of the X distribution? (Give answer accurate to 4 decimal places.) (c) For which of the two random samples, the one of part a) or the one of part b) İSX more likely to be within 01 cm of 1 1 cm? Explain your reasoning. x is more likely to be within .01 cm of 11 cm in sample (a) because of the decreased variability with a smaller sample size. 0 x is more likely to be within .01 cm of 11 cm in sample (a) because of the increased variability with a smaller sample size 0 x is more likely to be within .01 cm of 11 cm in sample (b) because of the decreased variability with a larger sample size 0 x is more likely to be within .01 cm of 11 cm in sample (b) because of the increased variability with a larger sample size You may need to use the appropriate table in the Appendix of Tables to answer this question. Need Help? Readt

Answer 1

a)

sampling distribution of Xbar centered =11 cm

std deviation of Xbar =standard deviation/sqrt(n)=0.03/sqrt(16)=0.0075

b)

sampling distribution of Xbar centered =11 cm

std deviation of Xbar =0.03/sqrt(64)=0.0038

c)

Xbar is more likely to be within 0.01 cm of 11 cm in sample (b) because of decreased variability with a larger sample size,