# You are planning to purchase a house that will require some renovations

**You MUST show all of your work to receive any credit.** If you have questions about showing work, please ask. Your work must be shown in a very neat presentation that is easily followed.

**Part 1. Be sure to clearly show all of your steps to each solution.**

You are planning to purchase a house that will require some renovations.

1. You will have a $400,000 mortgage for 20 years at the rate of 4.25%. What will your monthly payment be?

2. If you take the full term of the loan, how much interest will you have paid?

3. You decide to do some remodeling. You are looking at borrowing $7500 at the **simple interest** rate of 2% per year. You want to pay a maximum of $600 interest. How long will the loan need to be to meet this maximum interest of $600.00?

4. If you decide to put a $3000.00 bonus from your employment in a savings account that pays 2% interest **compounded monthly**, how much interest would you have earned after 4 years?

**Part 2**

A group of friends start a walking program. The chart below shows each member’s self-reported walking time in January 2022.

Person | Minutes Walking in January 2022 |

YOU |
350 |

B | 525 |

C | 400 |

D | 600 |

E | 150 |

F | 550 |

G | 300 |

H | 540 |

I | 425 |

K | 700 |

Answer the following questions based on this data. **Be sure to show all of your work for each question.**

1. What was the **mean** walking time for the group in January 2022? **If your answer is a decimal round to the nearest hundredth.**

2. By what percent did YOU exceed or fall below the mean in January 2022? __Express your__ __answer rounded to the nearest hundredth.__

3. What was the **median **walking time in January 2022?

**Part 3**

Here is data for a statistics class:

Final Grade | Women | Men |

A | 6 | 5 |

B | 7 | 8 |

C | 4 | 3 |

D | 2 | 1 |

F | 0 | 1 |

Answer the following questions based on the above data for the math class. **Be sure to show all of your work for each question.**

1. If one person is randomly chosen to participate in a focus group, what is the probability that the person will be a student who earned an A in the class?

2. A group of 6 students from this class is going to be randomly chosen to test a new video. In how many ways can the 6 students be chosen?

3. What is the probability that the random choice of the 6 students ( from b. above) will result in a group of all women being chosen?

**Part 4**

For this part, you will find it helpful to use a Venn diagram. You may submit a Venn diagram** or **thoroughly explain how you reached each answer.

In a math 105 class of 34 students, a survey showed that 20 students used the ALEKS e-text at least once, 7 used a video at least once, and 5 used both the e-text and a video at least once.

1. How many students used **only** the e-text?

2. How many students used **neither** the e-text nor the videos at least once?