Question

Project 4

This project asks you to make decisions based on what you have learned in this course so far. Each question below is worth 10 points. Some questions could be answered in different ways depending on your reasoning. You will not receive any credit for a question if you do not support your reasoning.

Please type your responses to each question following the prompts. Feel free to add space as needed. Attempt to stay orderly and put your answers in red font to make them easy to find.

1.              You are starting a donut shop. When you go to order a donut maker you find two choices with the               following information.

Machine 1:           $700, makes 500 donuts an hour with a standard deviation of 30 donuts per hour

Machine 2:           $700, makes 500 donuts an hour with a standard deviation of 60 donuts per hour

                  Which machine do you think you should purchase and why? Explain your reasoning and give the advantages          you get from that machine.

2.              The state gives two standardized tests in Math.

Test 1:                      The range of possible scores is 0 to 50.

Test 2:                      The range of possible scores is 0 to 100.

                  Which test would you expect to have a higher standard deviation? Why?

                  Does your expectation have to be true? Why?

3.              You do two studies.

Study 1:                  Compare the outside temperature to how much your heater runs

Study 2:                  Compare the outside temperature to how much your air conditioner runs

                  For each study, predict whether the correlation coefficient is positive or negative and why?

4.              You have two studies.

Study 1:                  Mean of 75 and standard deviation of 10

Study 2:                  Mean of 75 and standard deviation of 3

                  Without doing calculations, which study would have the higher probability for P(70<x<80)? Explain your choice.

5.              You calculate two probabilities from z-scores.

Probability 1:     P(z<1.25)

Probability 2:     P(z>1.25)

                  Which has the higher probability and why?

6.              You are given a z-score of -0.45. What can you say about the x-value in relationship to the mean?

7.              Based on the differences in chapter 6 and 7, which would have the higher probability when the mean is 10?            Explain your reasoning.

Probability 1:     P(8<x<12)

Probability 2:    

8.              Based on chapter 7, which study would have a higher probability for with a mean of 10?                    Explain you reasoning.

Study 1:                  n = 200

Study 2:                  n = 500

9.              The table lists the probability distribution for a certain game. Based on section 5.1, would you play the game?      Give your reasoning and show calculation.

Winnings	Probability
100	0.20
0	0.50
-100	0.30

Answer 1

Answer to 1)

Machine 1 has mean of 500 donuts with standard deviation of 30

And machine 2 has same mean of 500 donuts with standard deviation 60

Higher standard deviation implies more variance and lower standard deviation implies more consistency

When we talk about machines we always look for consistency

Hence a machine with lower standard deviation ( given same mean values) is always preferred in this scenario

.

Another way to come up with it is:

Coeffiicent of variation = (standard deviation / mean) *100

For machine 1

Coefficient of variation = (30/500) *100

Coefficient of variation = 6%

.

For machine 2

Coefficient of variation = (60 /500)*100

Coefficient of variation = 12%

.

It is considered that lower the value of coefficient of variation the more reliable the machine is. Hence Machine 1 is more reliable than machine 2