You are planning to purchase a house that will require a mortgage of $300,000.

 PLEASE SHOW THE WORK

PART 1

You are planning to purchase a house that will require a mortgage of $300,000.

You find 2 mortgage offers both at the same rate of 2.5%.  One is a 30-year mortgage and the other is a 20-year mortgage.

You know, without any computation, that the 30-year mortgage will have lower monthly payments than the 20-year mortgage since the rates are the same.  A friend advised that before taking the 30-year mortgage offer, you do some mathematical calculations to see if your budget can handle the extra amount of monthly payment for the 20-year mortgage.

1.  How much more money would you have to budget per month to make the monthly payments on the 20-year mortgage instead of the 30-year mortgage? 

2. You ask your friend what advantage there is to be paying more per month on the 20-year mortgage. Your friend replies that it is all about total interest.  What is the difference between the total interest you would pay on each mortgage?   Assume that you take the full term for each of the mortgages.

  

Part  2

You belong to two different walking groups.  Here is data about each group’s walking in January 2020. 

 

Group A

Person

Minutes Walking in January 2020

YOU

330

B

200

C

300

D

450

E

150

F

500

G

300

H

350

I

600

K

700

 

 

Group B

Person

Minutes Walking in January 2020

YOU

400

X

250

Y

500

Z

450

Q

650

R

600

 

Answer the following questions based on this data.

1. What was the Mean time walking for Group A and for Group B in January? (note you are finding two means times)

2. Did YOU exceed or fall below each group mean in January?  By what percent?

3. The recommendation is that we exercise 150 minutes per week.  For the purpose of this question, make the assumption that January is 4 weeks. The recommendation would then translate to 600 minutes in January. Did you exceed or fall below the recommendation in January? (note : add your walking time from each group in order to answer this question.)

4. Lets suppose you want to draw a pie chart that shows information for the member 0f each group classified by a rating based on the amount of walking time. (note  you do not have to draw the pie chart)

Excellent will be the category for the percentage of group members who walked for 600 or more minutes.  

Very Good will be the category for the percentage of group members who walked for 500 – 599 minutes.  

Good will be the category for the percentage of group members who walked for 499 – 400 minutes.    

Needs Improvement will be the category for the percentage of group members who walked for less than 400 minutes.  

  A) On which pie chart, the group A pie chart or the group B pie chart, will the excellent category percentage      be greater?  What is that percentage?  

B) On which pie chart will the Needs Improvement category percentage be greater?  What is that percentage? 

5. One other way to look at the data is by percentiles.  What was your percentile rank in each group?

Part 3 

The grades for a Statistics class were as follows:  5 A’s;    7 B’s;    10 C’s;    3 D’s;    1 F

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. If one person is randomly chosen to participate in a focus group, what is the probability that the student chosen will NOT have earned an F?

3. If one person is randomly chosen what is the probability that the students will have earned either a C or a D? 

4. What is the probability that the random selection of two students for the focus group will result in one A student and one B student?