The inside diameter of a randomly selected piston ring is a random variable with ean value 12 cm and standard deviation .04 cm. If X is the sample mean diameter for a random sample of n= 16 rings, where is the sampling distribution of X centered, and what is the standard deviation of the X distribution? Answer the questions posed in part (a) for a sample size of n = 64 rings. For which of the two random samples, the one of part (a) or the one of part (b), is X more likely to be within .01 cm of 12 cm? Explain your reasoning.
The inside diameter of a randomly selected piston ring is a random variable with ean value 12 cm and standard deviation .04 cm. If X is the sample mean diameter for a random sample of n= 16 rings, where is the sampling distribution of X centered, and what is the standard deviation of the X distribution? Answer the questions posed in part (a) for a sample size of n = 64 rings. For which of the two random samples, the one of part (a) or the one of part (b), is X more likely to be within .01 cm of 12 cm? Explain your reasoning.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 14PPS
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The inside diameter of a randomly selected piston ring is a random variable with
mean value 12 cm and standard deviation .04 cm.
a. If ? ̅
is the sample mean diameter for a random sample of n= 16 rings, where is
the sampling distribution of ? ̅
centered, and what is the standard deviation of
the ? ̅
distribution?
b. Answer the questions posed in part (a) for a sample size of n = 64 rings.
c. For which of the two random samples, the one of part (a) or the one of part (b),
is ? ̅
more likely to be within .01 cm of 12 cm? Explain your reasoning.
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