**Cell Phone Lifetimes**A recent study of the lifetimes of cell phones found the average is 23.2 months. The standard deviation is 3.1 months. If a company provides 33 employees with a cell phone, find the probability that the mean lifetime of these phones will be less than 23.8 months. Assume cell phone life is a normally distributed variable, the sample is taken from a large population, and the correction factor can be ignored. Use a TI-83 Plus/TI-84 Plus calculator. Round your answer to at least four decimal places.\[ P\left(\overline{X} < 23.8\right) = \square\]### Instructions:To solve this problem, follow these steps:1. **Calculate the Standard Error (SE):**\[ \text{SE} = \frac{\sigma}{\sqrt{n}} \] - Standard deviation ($ \sigma $) = 3.1 months - Sample size ($ n $) = 33 employees2. **Determine the Z-score:**\[ Z = \frac{\overline{X} - \mu}{SE} \] - Mean ($ \mu $) = 23.2 months - Target mean ($ \overline{X} $) = 23.8 months3. **Find the Probability:** - Once the Z-score is calculated, use a Z-table or a calculator to find the corresponding probability.### Example Calculation:1. **Standard Error (SE):**\[ \text{SE} = \frac{3.1}{\sqrt{33}} \approx 0.5394 \]2. **Z-score:**\[ Z = \frac{23.8 - 23.2}{0.5394} \approx 1.113 \]3. **Probability:** - Using a Z-table or calculator, find the probability corresponding to Z = 1.113. ### TI-83 Plus/TI-84 Plus Calculator Steps:1. **Press 2nd/DISTR**2. **Select normalcdf**3. **Enter (-E99, 23.8, 23.2, 0.5394)** and press ENTERThis will give you the probability that the average lifetime of 33 cell phones is less than 23.8 months

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Cell Phone Lifetimes A recent study of the lifetimes of cell phones found the average is 23.2 months. The standard deviation is 3.1 months. If a company provides its 33 employees with a cell phone, find the probability that the mean lifetime of these phones will be less than 23.8 months. Assume cell phone life is a normally distributed variable, the sample is taken from a large population, and the correction factor can be ignored. Use a TI-83 Plus/TI-84 Plus calculator. Round your answer to at least four decimal places. P(X<23.8)=

Cell Phone Lifetimes A recent study of the lifetimes of cell phones found the average is 23.2 months. The standard deviation is 3.1 months. If a company provides its 33 employees with a cell phone, find the probability that the mean lifetime of these phones will be less than 23.8 months. Assume cell phone life is a normally distributed variable, the sample is taken from a large population, and the correction factor can be ignored. Use a TI-83 Plus/TI-84 Plus calculator. Round your answer to at least four decimal places. P(X<23.8)=

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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