### Chimney Rock Hospital Task Completion Time Analysis**Objective:**To analyze the time it takes on average for a nurse at the Chimney Rock Hospital in North Carolina to complete a specific task. The completion time is normally distributed with a mean of 13.7 minutes and a standard deviation of 3.4 minutes.**Questions:**1. **Proportion of Nurses Completing Tasks Between 15.2 and 17.7 Minutes** - We want to determine the proportion of nurses who complete a task within this time frame. 2. **Proportion of Nurses Completing Task in Less Than 8 Minutes and 24 Seconds** - We are interested in the proportion of nurses who finish a task in less than 8 minutes and 24 seconds.3. **Completion Time at the 73rd Percentile** - We need to find out what the task completion time is at the 73rd percentile.4. **Probability of Sample Mean Time Greater Than 14 Minutes and 12 Seconds** - We want to calculate the probability that the sample mean time for 30 randomly selected nurses is greater than 14 minutes and 12 seconds. **Data:**- Mean completion time (μ): 13.7 minutes- Standard deviation (σ): 3.4 minutes- Time and proportions to investigate: - Between 15.2 and 17.7 minutes - Less than 8 minutes, 24 seconds - 73rd percentile completion time - Sample mean time greater than 14 minutes, 12 seconds for n = 30 nurses---#### Detailed Breakdown:**a. Proportion of Nurses Completing Tasks Between 15.2 and 17.7 Minutes:**To solve this:- Convert the times (15.2 and 17.7 minutes) to Z-scores using the formula: \[ Z = \frac{(X - μ)}{σ} \]- Look up these Z-scores in the standard normal distribution table to find the corresponding proportions.**b. Proportion of Nurses Completing Task in Less Than 8 Minutes and 24 Seconds:**To solve this:- Convert 8 minutes and 24 seconds to a decimal (8.4 minutes).- Calculate the Z-score for 8.4 minutes.- Use the Z-score to find the corresponding proportion from the standard normal distribution table.**c. Completion Time at

Given: Mean μ=13.7 minutes Standard deviation σ=3.4

Answered: 5. Suppose that it takes a nurse at the…

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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