**Problem Statement:**The total of individual weights of garbage discarded by 15 households in one week is normally distributed with a mean of 32.1 lbs and a sample standard deviation of 14.3 lbs. Find the 99% confidence interval of the mean.**Solution:**1. **Calculate the standard error (SE)** \[ SE = \frac{\text{sample standard deviation}}{\sqrt{n}} \] Where: - Sample standard deviation (s) = 14.3 lbs - n (sample size) = 15 \[ SE = \frac{14.3}{\sqrt{15}} \]2. **Find the critical value for the 99% confidence level** Since the sample size is small (< 30), we use the t-distribution. Using a t-table or calculator: Degrees of freedom (df) = n - 1 = 15 - 1 = 14 For a 99% confidence level and 14 degrees of freedom, the critical value (t*) is approximately: \[ t^* \approx 2.977 \]3. **Calculate the margin of error (ME)** \[ ME = t^* \times SE \]4. **Determine the confidence interval** The confidence interval is given by: \[ \text{mean} \pm ME \]**Note:**- Do not round in between steps.- Round final answers to at least 4 decimal places.**Input Fields:**\[ \left\langle \text{Lower Bound} \ \boxed{\text{Select an answer}} \ \text{Upper Bound} \right\rangle \]**Rounding Instruction:**Do not round in between steps. Round answers to at least 4 decimal places.

Answered: Image /qna-images/answer/795ef105-8098-4965-b71f-670ad34bb337.jpg

The total of individual weights of garbage discarded by 15 households in one week is normally distributed with a mean of 32.1 lbs with a sample standard deviation of 14.3 lbs. Find the 99% confidence interval of the mean. Select an answer v < Do not round in between steps. Round answers to at least 4 decimal places.

The total of individual weights of garbage discarded by 15 households in one week is normally distributed with a mean of 32.1 lbs with a sample standard deviation of 14.3 lbs. Find the 99% confidence interval of the mean. Select an answer v < Do not round in between steps. Round answers to at least 4 decimal places.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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