Thank you for visiting The mean time to assemble a piece of furniture is 52 minutes Suppose the assembly times are normally distributed with a standard deviation of 4. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Final answer:
Between 99.7% of the assembly times fall between 39.1 minutes and 64.9 minutes.
Explanation:
To find the range within which 99.7% of the assembly times fall, we can use the Empirical Rule.
The Empirical Rule states that for a normal distribution, approximately 68% of the values fall within one standard deviation of the mean, 95% fall within two standard deviations, and 99.7% fall within three standard deviations.
In this case, the mean is 52 minutes and the standard deviation is 4.3 minutes. Three standard deviations above and below the mean would give us a range of:
- 52 minutes - (3 * 4.3 minutes) = 52 minutes - 12.9 minutes = 39.1 minutes
- 52 minutes + (3 * 4.3 minutes) = 52 minutes + 12.9 minutes = 64.9 minutes
Therefore, between 99.7% of the assembly times fall between 39.1 minutes and 64.9 minutes.
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