Answered: According to a certain organization,…

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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$Certainly! Here is the transcription of the given image, formatted for an educational website: --- ### Statistical Analysis Exercise **Problem Statement:** According to a study, the mean lifespan of a certain brand of bulb is $ \mu = 1741 $ hours. Assume the population standard deviation is $ \sigma = 350 $ hours and that a random sample of 50 bulbs is tested. Complete the tasks in the following exercise: --- **Tasks:** a) **Calculate the standard error of the mean.** (Round to two decimal places as needed.) b) **What is the probability that the sample mean will be more than 1720 hours?** $ P(\bar{X} > 1720) = $ (Round to four decimal places as needed.) c) **What is the probability that the sample mean will be between 1680 and 1710 hours?** $ P(1680 < \bar{X} < 1710) = $ (Round to four decimal places as needed.) d) **Would a sample mean of 1736.3 hours support the claim made by the organization?** (Round to two decimal places as needed.) - **A.** _The probability $ P(\bar{X} \leq 1736.3) = $_ _This supports the claim._ - **B.** _The probability $ P(\bar{X} \geq 1736.3) = $_ _This contradicts the claim._ e) **Identify the symmetrical interval that includes 95% of the sample means if the population mean is 1741 hours.** \[ \text{_____ hours} \leq \bar{X} \leq \text{_____ hours} \] (Round to one decimal place as needed.) **Instructions:** Select the correct choice below and fill in the answer box within your choice. --- Ensure all calculations are performed using appropriate statistical techniques and rounding rules as specified in each task.$

Transcribed Image Text:Certainly! Here is the transcription of the given image, formatted for an educational website: --- ### Statistical Analysis Exercise **Problem Statement:** According to a study, the mean lifespan of a certain brand of bulb is $ \mu = 1741 $ hours. Assume the population standard deviation is $ \sigma = 350 $ hours and that a random sample of 50 bulbs is tested. Complete the tasks in the following exercise: --- **Tasks:** a) **Calculate the standard error of the mean.** (Round to two decimal places as needed.) b) **What is the probability that the sample mean will be more than 1720 hours?** $ P(\bar{X} > 1720) = $ (Round to four decimal places as needed.) c) **What is the probability that the sample mean will be between 1680 and 1710 hours?** $ P(1680 < \bar{X} < 1710) = $ (Round to four decimal places as needed.) d) **Would a sample mean of 1736.3 hours support the claim made by the organization?** (Round to two decimal places as needed.) - **A.** _The probability $ P(\bar{X} \leq 1736.3) = $_ _This supports the claim._ - **B.** _The probability $ P(\bar{X} \geq 1736.3) = $_ _This contradicts the claim._ e) **Identify the symmetrical interval that includes 95% of the sample means if the population mean is 1741 hours.** \[ \text{_____ hours} \leq \bar{X} \leq \text{_____ hours} \] (Round to one decimal place as needed.) **Instructions:** Select the correct choice below and fill in the answer box within your choice. --- Ensure all calculations are performed using appropriate statistical techniques and rounding rules as specified in each task.

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