A manufacturer knows that their items have a lengths that are skewed right, with a mean of 5.9 inches, and standard deviation of 1 inches. If 31 items are chosen at random, what is the probability that their mean length is greater than inches? (Round answer to four decimal places)

A First Course in Probability (10th Edition)
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Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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**Problem Statement:**

A manufacturer knows that their items have lengths that are skewed right, with a mean of 5.9 inches, and standard deviation of 1 inch. If 31 items are chosen at random, what is the probability that their mean length is greater than 6.3 inches?

*Instructions: Round answer to four decimal places.*

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This problem involves statistical inference, specifically the calculation of probabilities related to the sample mean. In this case, we are examining a sample of size 31 from a population with known parameters (mean and standard deviation) and are tasked with finding the probability that the sample mean exceeds a certain value.

To solve this, one would typically use the Central Limit Theorem to approximate the sampling distribution of the sample mean with a normal distribution, despite the skewness of the population distribution.
Transcribed Image Text:**Problem Statement:** A manufacturer knows that their items have lengths that are skewed right, with a mean of 5.9 inches, and standard deviation of 1 inch. If 31 items are chosen at random, what is the probability that their mean length is greater than 6.3 inches? *Instructions: Round answer to four decimal places.* --- This problem involves statistical inference, specifically the calculation of probabilities related to the sample mean. In this case, we are examining a sample of size 31 from a population with known parameters (mean and standard deviation) and are tasked with finding the probability that the sample mean exceeds a certain value. To solve this, one would typically use the Central Limit Theorem to approximate the sampling distribution of the sample mean with a normal distribution, despite the skewness of the population distribution.
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