R Markdown

This is an R Markdown document. Markdown is a simple formatting syntax for authoring HTML, PDF, and MS Word documents. For more details on using R Markdown see http://rmarkdown.rstudio.com.

When you click the Knit button a document will be generated that includes both content as well as the output of any embedded R code chunks within the document. You can embed an R code chunk like this:

summary(cars)
##      speed           dist       
##  Min.   : 4.0   Min.   :  2.00  
##  1st Qu.:12.0   1st Qu.: 26.00  
##  Median :15.0   Median : 36.00  
##  Mean   :15.4   Mean   : 42.98  
##  3rd Qu.:19.0   3rd Qu.: 56.00  
##  Max.   :25.0   Max.   :120.00

Including Plots

You can also embed plots, for example:

Note that the echo = FALSE parameter was added to the code chunk to prevent printing of the R code that generated the plot. // Add toggle functionality for all solution sections document.addEventListener(‘DOMContentLoaded’, function() { const toggleButtons = document.querySelectorAll(‘.solution-toggle’); toggleButtons.forEach(button => { button.addEventListener(‘click’, function() { const solution = this.nextElementSibling; if (solution.style.display === ‘none’ || solution.style.display === ’‘) { solution.style.display = ’block’; this.innerHTML = ‘🔽 Hide Excel Solution’; } else { solution.style.display = ‘none’; this.innerHTML = ‘▶️ Show Excel Solution’; } }); }); }); ## Question 1

What is the sum of 25 + 75?

A soft drink bottling plant must comply with FDA regulations requiring bottles to be filled between 490 ml and 515 ml. The current process has:

Mean fill volume (μ) = 500 ml Standard deviation (σ) = 5 ml Daily production = 50,000 bottles Operating days/year = 250 Cost of wasted materials = $0.50/bottle Managerial Questions:

What percentage of bottles comply with FDA specifications? How many bottles fail daily and annually? What is the annual waste cost? To achieve less than 1% waste, management considers two options: Option A: Recalibrate machines to shift the mean (one-time cost: $20,000)

Option B: Install precision sensors to reduce variability (one-time cost: $50,000)

Which option should the plant choose?