Use the material from the case below and the attached file to complete this project.

Your company makes ropes used for camping and scouting. The ropes are sold as part of tent kits and individually for the scouts to learn how to tie knots. The manufacturing process is supposed to create ropes 84cms long. As the process is not always accurate, the acceptable range for the ropes length is 83.75cms to 84.2cms. Each hour 30 ropes are randomly selected as they come off the line and measured. A week’s worth of samples are provided in the attached file.

Part 1

Calculate the Mean, Median, Mode, Standard Deviation, and Covariance for each sample.

What is the range of the means? Are any of the means exactly equal to 84?

What may happen in the manufacturing process that would result in ropes that are not 84cms long?

Part 2

What is the probability for each sample that a rope is outside 2 standard deviations (above or below) the sample mean?

What is the probability of having ropes made below the acceptable range during (hint you will need to take the data from all samples that meet the asked about criteria):

The first hour of the morning?

The hour after coming back from lunch?

The last hour before going home?

What is the probability of having ropes that are above 84.20cms being made (hint you will need to take the data from all samples that meet the asked about criteria):

Before lunch

After Lunch

Part 3

Create a table that shows the Probability Distribution of the Number of Rope Errors (outside the acceptable range) per Day. Then compute the expected value of the Number of ropes made outside of the range.

Evaluate the properties required for the Poisson Distribution on page 189. Explain why or why not it would be appropriate to use the Poisson Distribution on the data we have collected.

On a separate sheet in the Excel file labeled Z scores, convert all the sample data points to Z scores.

Submit your answers and calculations in one Excel file.

Data Link