Please answer all questions sepretly: Bottle Caps 

A machine produces bottle caps.  The machine is calibrated to produce bottle caps with a mean diameter of 2.8 cm and standard deviation of 0.03 cm.  Let X represent the random variable for diameter of bottle caps.   Leave your answers as a percent without rounding.  

1. What percent of bottle caps are between 2.77 cm and 2.83 cm?

2. Find P(2.74 ≤ x ≤ 2.86) 

3. What percent of bottle caps are less than 2.71 cm?  

4. Find P(X ≥ 2.86) 

5. What percent of bottle caps are exactly 2.8 cm? 

6. If all caps that are smaller than 2.71 cm and greater than 2.89 cm are rejected/thrown out, what percent would be lost?

These are about the frequency polyon:

7.Does the total area under a probability density equal 1. 

 

8.Does the total area under the relative frequency polygon equal 1 if the interval size is 1? 

 

9.Do smaller interval sizes always allow you to get a smoother polygon that will better represent the data? 

 

10.Is the interval size chosen when the difference between the polygon and the histogram bars is as small as possible? 

11. Does the interval size depend on the number of data points? 

 

 

 

3 years ago

Answered By Sara S

Hi there, 

Typing here is a little hard for me because I used to Latex. 

Please use the uploaded pdf using the following link:

 

https://www.yumpu.com/en/document/view/63343067/bottle-caps

 

Enjoy!

Sara Sasani

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