Answered: The amounts of nicotine in a certain…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

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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$### Educational Website Content #### Statistical Analysis of Nicotine Levels in Cigarettes The nicotine content in a specific brand of cigarette is normally distributed with a mean of 0.961 g and a standard deviation of 0.318 g. The manufacturer claims to have reduced the nicotine content. To support this, a sample of 45 cigarettes showed a mean nicotine content of 0.866 g. **Objective:** Determine the probability of obtaining a sample with a mean of 0.866 g or less, assuming the mean and standard deviation have not changed. **Calculation:** - Find $ P(\overline{x} \leq 0.866) $. - Provide your answer accurate to four decimal places. **Question:** Based on this result, is it valid to claim that the nicotine amount is lower? - **No.** The probability of obtaining this data is sufficiently high to have occurred by chance. - **Yes.** The probability of this data occurrence is unlikely by chance alone. **Instructions:** 1. Calculate the probability. 2. Evaluate if the manufacturer’s claim is statistically significant. **Graph/Diagram Explanation:** There are no graphs or diagrams in this content. Ensure to rely on normal distribution tables or statistical software for calculations. **Submit Your Answer:** A "Submit Question" button is provided for students to enter their probability calculation.$

Transcribed Image Text:### Educational Website Content #### Statistical Analysis of Nicotine Levels in Cigarettes The nicotine content in a specific brand of cigarette is normally distributed with a mean of 0.961 g and a standard deviation of 0.318 g. The manufacturer claims to have reduced the nicotine content. To support this, a sample of 45 cigarettes showed a mean nicotine content of 0.866 g. **Objective:** Determine the probability of obtaining a sample with a mean of 0.866 g or less, assuming the mean and standard deviation have not changed. **Calculation:** - Find $ P(\overline{x} \leq 0.866) $. - Provide your answer accurate to four decimal places. **Question:** Based on this result, is it valid to claim that the nicotine amount is lower? - **No.** The probability of obtaining this data is sufficiently high to have occurred by chance. - **Yes.** The probability of this data occurrence is unlikely by chance alone. **Instructions:** 1. Calculate the probability. 2. Evaluate if the manufacturer’s claim is statistically significant. **Graph/Diagram Explanation:** There are no graphs or diagrams in this content. Ensure to rely on normal distribution tables or statistical software for calculations. **Submit Your Answer:** A "Submit Question" button is provided for students to enter their probability calculation.

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