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A manufacturer knows that their items have a lengths that are skewed right, with a mean of 19.6 inches, and standard deviation of 0.5 inches. If 45 items are chosen at random, what is the probability that their mean length is greater than 19.6 inches? (Round answer to four decimal places)

A manufacturer knows that their items have a lengths that are skewed right, with a mean of 19.6 inches, and standard deviation of 0.5 inches. If 45 items are chosen at random, what is the probability that their mean length is greater than 19.6 inches? (Round answer to four decimal places)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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**Question: Analyzing the Probability of Item Lengths** A manufacturer knows that their items have lengths that are skewed right, with a mean of 19.6 inches and a standard deviation of 0.5 inches. If 45 items are chosen at random, what is the probability that their mean length is greater than 19.6 inches? *(Round answer to four decimal places)* --- **Explanation:** In this problem, we are dealing with a sample mean and using the Central Limit Theorem to approximate the probability. The information given tells us that the lengths of the items are not normally distributed (they are skewed to the right), but with a large enough sample size (n = 45), the sampling distribution of the sample mean can be approximated by a normal distribution. Key Parameters: - Population mean (μ): 19.6 inches - Population standard deviation (σ): 0.5 inches - Sample size (n): 45 To find the probability that the sample mean length is greater than 19.6 inches, we need to standardize the sample mean and use the Z-score formula.
Transcribed Image Text:**Question: Analyzing the Probability of Item Lengths** A manufacturer knows that their items have lengths that are skewed right, with a mean of 19.6 inches and a standard deviation of 0.5 inches. If 45 items are chosen at random, what is the probability that their mean length is greater than 19.6 inches? *(Round answer to four decimal places)* --- **Explanation:** In this problem, we are dealing with a sample mean and using the Central Limit Theorem to approximate the probability. The information given tells us that the lengths of the items are not normally distributed (they are skewed to the right), but with a large enough sample size (n = 45), the sampling distribution of the sample mean can be approximated by a normal distribution. Key Parameters: - Population mean (μ): 19.6 inches - Population standard deviation (σ): 0.5 inches - Sample size (n): 45 To find the probability that the sample mean length is greater than 19.6 inches, we need to standardize the sample mean and use the Z-score formula.
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