Statistics and Finance

Exercises 4.1           
Problem 4: 
To study the spending habits of shoppers in Orlando, Florida, 50 randomly selected shoppers at a mall were surveyed to determine the number of credit cards they carried. The following results were obtained:
2 5 0 4 2 1 0 6 3 5 4 3 4 0
5 2 5 2 0 2 5 0 2 5 2 5 4 3
5 6 1 0 6 3 5 3 4 0 5 2 2 5
2 0 2 0 4 2 1 0
a)	Organize the given data by creating a frequency distribution
b)	Construct a pie chart to represent the data
c)	Construct a histogram using single-valued classes of data

Problem 20:
The following lists the types of accidental deaths in the United States in 2000. Construct a pie chart to represent the data.
TYPE OF ACCIDENT	NUMBER OF DEATHS
Motor vehicle			43,000
Falls				16,200
Poison				12,100
Drowning			3,900
Fire				3,600
Choking			3,400
Firearms			600

Exercises 4.3           
Problem 8:
Paki surveyed the price of unleaded gasoline (self-serve) at gas stations in Novato and Lafayette. The raw data, in dollars per gallon, are as follows:
NOVATO:  		1.309	1.289	1.339	1.309	1.259	1.239
LAFAYETTE:	1.329	1.269	1.189	1.349	1.289	1.229
a)	Find the mean price in each city. Which city has the lowest mean?
b)	Find the standard deviation of prices in each city
c)	Which city has more consistently priced gasoline? Why?

Problem 16:
Amy surveyed the prices for a quart of a certain brand of motor oil. The sample data, in dollars per quart, is summarized below:
Price Per Quart	Number of Stores
0.99			2
1.09			5
1.19			10
1.29			13
1.39			9
1.49			3
a)	Find the mean and the standard deviation of the prices
b)	What percent of the data lies within one standard deviation of the mean?
c)	What percent of the data lies within two standard deviations of the mean?
d)	What percent of the data lies within three standard deviations of the mean?

Problem 20:
The age composition of the population of the United States in the year 2000 is given below. Replace the interval “85 and over” with the interval 85  ≤  x  ≤  100 and find the standard deviation of all people in the United States.
AGE			NUMBER OF PEOPLE (in thousands)
0 < x < 5		19,176
5 ≤ x ≤ 10		20,550
10 ≤ x < 15		20,528
15 ≤ x < 25		39,184
25 ≤ x < 35		39,892
35 ≤ x < 45		44,149
45 ≤ x < 55		37,678
55 ≤ x < 65		24,275
65 ≤ x < 85		30,752
85 and over		4,240 

Exercises 4.4           
Problem 6:
A population is normally distributed with mean 18.9 and a standard deviation 1.8
a)	Find the intervals representing one, two, and three standard deviations of the mean
b)	What percentage of the data lies in each of the intervals in part a?
c)	Draw the bell curve

Exercises 5.1           
Problem 38:
Sam Needham bought a house from Sheri Silva for $238,300. In lieu of a 20% down payment, Ms. Silva accepted a 10% down payment at the time of the sale and a promissory note from Mr. Needham for an additional 10%, due in four years. Mr. Needham also agreed to make monthly interest payments to Ms. Silva at 9% interest until the note expires. Mr. Needham obtained a loan from his bank for the remaining 80% of the purchase price. The bank in turn paid Ms. Silva the remaining 80% of the purchase price, less a sales commission (6% of the purchase price) paid to the sellers’ and the buyers’ real estate agents.
a)	Find Mr. Needham’s down payment
b)	Find the amount that Mr. Needham borrowed from his bank
c)	Find the amount that Mr. Needham borrowed from Ms. Silva
d)	Find Mr. Needham’s monthly interest payment to Ms. Silva
e)	Find Ms. Silva’s total income from all aspects of the down payment (including the down payment, the amount borrowed under the promissory note, and the monthly payments required by the promissory note).
f)	Find Ms. Silva’s income from Mr. Needham’s bank.
g)	Find Ms. Silva’s total income from all aspects of the sale.

Exercises 5.2           
Problem 6:
Find the periodic rate that corresponds to the given compound rate below if the rate is compounded a) quarterly, b) monthly, c) daily, d) bi-weekly (every two weeks), and e) semi-monthly (twice a month).
Do not round off the periodic rate.
Compound Rate: 10.1%

Exercises 5.3           
Problem 36:
Chrissy Fields buys some land in Oregon. She agrees to pay the seller a lump sum of $120,000 in six years. Until then, she will make monthly simple interest payments to the seller at 12% interest.

a)	Find the amount of each interest payment
b)	Chrissy sets up a sinking fund to save the $120,000. Find the size of her semiannual payments if her money earns 10 ¾ % interest.
c)	Prepare a table showing the amount in the sinking fund after each deposite.

Exercises 5.4           
Problem 10:
Shirley Trembley bought a house for $187,600. She put 20% down and obtained a simple interest amortized loan for the balance at 6 3/8% for 30 years.
a)	Find her monthly payment
b)	Find the total interest
c)	Prepare an amortization schedule for the first two months of the loan
d)	Most lenders will approve a home loan only if the total of all the borrower’s monthly payments, including the home loan payment, is no more than 38% of the borrower’s monthly income. How much must Ms. Trembley make to qualify for the loan?