The inside diameter of a randomly selected piston ring is a random variable with mean value 12 cm and standard deviation 0.04 cm. (a) 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? (b) Answer the question 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 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 mean value 12 cm and standard deviation 0.04 cm. (a) 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? (b) Answer the question 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 X more likely to be within .01 cm of 12 cm? Explain your reasoning.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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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 0.04 cm.
(a) 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?
(b) Answer the question 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 X more likely to be within .01 cm of 12 cm?
Explain your reasoning.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd75f698c-532c-4f8e-87a8-3cbbb0dc5f79%2F99c2605c-13de-45bf-b6b9-32f0379ddc2c%2Fg08uyqk_processed.png&w=3840&q=75)
Transcribed Image Text:The inside diameter of a randomly selected piston ring is a random
variable with mean value 12 cm and standard deviation 0.04 cm.
(a) 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?
(b) Answer the question 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 X more likely to be within .01 cm of 12 cm?
Explain your reasoning.
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