Instructor-created question -Question Help * Suppose that a machine cuts lumber

Question

Instructor-created question -Question Help * Suppose that a machine cuts lumber to a mean length of 8 feet (96 inches) with a standard deviation of 0.6 inch. You randomly select 45 boards and find that the mean length is 96.2 inches. Complete parts (a) through (d) (a) State the Central Limit Theorem. O A. For any population distribution, with a sufficiently large sample, the sample means will be normally distributed. O B. For any population distribution, regardless of the sample size, the sample means will be normally distributed. O c. For any population distribution, with a surficiently large sample, the population means will be normally distributed O D. For any population distribution, with a sufficiently large sample, the sample means will not be normally distributed (b) What is the sampling distribution of x based on the theorem? O A. The distribution of the sample mean is skewed to the right O B. The distribution of the sample mean cannot be determined based on the information provided O C. The distribution of the sample mean is skewed to the left. O D. The distribution of the sample mean is approximately normal. (c) What are the mean and standard deviation of i (round the standard deviation to 5 decimal places, as needed) (d) What is the probability that the mean of the sample is 96.2 inches or more? (Round to four decimal places as needed.)

Explanation / Answer

(a) For Central limit theorem, OPtion A is correct.

(b) Option D is correct as distribution of sample mean will be approximately normal.

(c) Mean x  = 96 inches ; x  = /sqrt(n)= 0.6/sqrt(45) = 0.08944 inch

(d) Pr(x > 96.2 inches) = 1 - NORM (x < 96.2 inches ; 96 inch ; 0.08944 inch)

Z = (96.2 - 96)/0.08944 = 2.236

Pr(x > 96.2 inches) = 1 - NORM (x < 96.2 inches ; 96 inch ; 0.08944 inch) = 1 - Pr(Z < 2.236) = 1 - 0.9873 = 0.0127

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