Question

2. (25 Points) The inside diameter of a randomly selected piston ring is a random variable with mean value 12.00 cm and standard deviation 0.04 cm. (a) If $\bar{X}$ is the sample mean diameter for a random sample of $n = 16$ rings, where is the sampling distribution of $\bar{X}$ centered, and what is the standard deviation of the $\bar{X}$ distribution? (b) Answer the questions posed in part (a) for a sample of size $n = 64$ rings. (c) For which of the two random samples, the one of part (a) or the one of part (b), is $\bar{X}$ more likely to be within 0.01 cm of 12 cm? Explain your reasoning. (d) Now assume that distribution of the inside diameter is normal. Calculate $P(11.99 \leq \bar{X} \leq 12.01)$ when $n = 16$. (e) Still assuming that the distribution of the inside diameter is normal, how likely is it that the sample mean diameter exceeds 12.01 when $n = 25$?

          2. (25 Points) The inside diameter of a randomly selected piston ring is a random variable with mean value 12.00 cm and standard deviation 0.04 cm.

(a) If $\bar{X}$ is the sample mean diameter for a random sample of $n = 16$ rings, where is the sampling distribution of $\bar{X}$ centered, and what is the standard deviation of the $\bar{X}$ distribution?

(b) Answer the questions posed in part (a) for a sample of size $n = 64$ rings.

(c) For which of the two random samples, the one of part (a) or the one of part (b), is $\bar{X}$ more likely to be within 0.01 cm of 12 cm? Explain your reasoning.

(d) Now assume that distribution of the inside diameter is normal. Calculate $P(11.99 \leq \bar{X} \leq 12.01)$ when $n = 16$.

(e) Still assuming that the distribution of the inside diameter is normal, how likely is it that the sample mean diameter exceeds 12.01 when $n = 25$?

2 25 points the inside diameter of a randomly selected piston ring is a random variable with mean value 1200 cm and standard deviation 004 cm a if barx is the sample mean diameter for a rand 59926

Added by Frank H.

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