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 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)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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.*
---
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F828fe599-f033-4e13-bbc5-938fe3ceb9f0%2Fb6e433b4-409e-4953-adbd-7207d8bffb92%2F3kt5dhb_processed.jpeg&w=3840&q=75)
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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