Download BUS 205/BUS 305 Skill Set

BUS 305 Skill Set
These problems are typical of some of the kinds of mathematical exercises you will need to be
able to do to be successful in your business statistics classes. We suggest you reserve about an
hour, grab a pencil, some scratch paper, and your calculator, and see how you do. The answers
appear at the end. Problems 1 –14 are general review; problems 15 – 22 include concepts
specific to BUS 305.
1.
Convert .237 to a percent.
2.
Convert 37.5% to a decimal.
3.
Convert 5/7 to both a percent and a decimal.
4.
Sales in 2004 were $52.37 million and sales in 2003 were $48.09 million. Express the
2004 sales as a percent of the 2003 sales. What is the percent increase in sales from 2003 to
2004?
5.
Put these numbers in order from lowest to highest.
-5, 3, 18, |-2|, -1,
6.
-1.1, -1.01,
1,
1.1
Put these numbers in order from lowest to highest.
1/2, 1/3, 5/6, 3/8
7.
Fill in the blank in each expression with the proper symbol: either < or >
5 ___ 3
-5 ___ 3
-5 ___ -3
-1.11 ___ -1.12
-1.11 ___ -1.10
8.
Evaluate
9.
Evaluate
14.36 
2.6
(8  2.16) 2
5
3
5( 2  ) 2
2
10.
As the purchasing agent for your organization, you want to buy components at the best
price possible, as long as the quality is comparable. From which company will you get the best
price for ordering 1200 units?
The price from Supplier A is given by this table.
If the order quantity is
the price for each unit is
0 – 499
$5.00
500 – 999
$4.50
1000 or more
$4.00
The price from Supplier B is
$6.00 per unit for the first 200 units
$4.00 per unit for the next 500 units
$3.00 per unit for the next 1000 units
11.
Compute the answers for each of these expressions
a.
1 3

2 7
b.
2 *3* 4
5*8
c.
6(5 x  2)
3
d.
5 3

x 2x
e.
(5) 2
f.
(4) 1 / 2
g.
(4) 1 / 2
12.
A major research study looks at the average price of a prescription drug. Records from
5000 transactions are considered. The price per prescription ranges from $13.12 to $47.38.
Which of the following could not be the average price of the 5000 prescriptions and why?
a.
b.
c.
$5000
$8.65
$41.19
Can you tell which of these is the average price?
d.
e.
f.
$47.38
$25.25
$53.29
13.
14.
Solve each of these expressions for x:
a.
5x – 3 = 12
b.
2x + 1 > x – 5
c.
4x + 2 < 7x – 4
Calculate (18 + 2(12))(1.07)
Problems 15 through 22 deal with concepts you will need for BUS 305.
Use the graph below to help you answer questions 15 through 18.
12
10
8
6
4
2
0
-4
-3
-2
-1
-2
0
1
2
3
4
5
-4
-6
15.
As x gets larger, what happens to y?
16.
For each of the ordered pairs below, indicate whether or not the point lies on the line.
a.
b.
c.
(-1, 0)
(-1, 2)
(2, 0)
17.
What is the slope of the line?
18.
Which equation matches the graph?
y = 2x + 2
y=x+2
y = -1x + 2
y = x2
d.
e.
f.
(0, 2)
(1, 4)
(0, 0)
19.
Use this data to calculate the following:
x
4
3
5
1
2
a.
b.
c.
d.
e.
y
1
2
0
6
5
x
x
 x 
 xy
 x y
2
2
20.
A product sells for $300 per unit. Let x be the number of units sold. Write an expression
for the revenue obtained from selling x units.
The cost to make x units includes both a fixed portion and a variable portion and is given
by the expression 200x + 10000.
Profit is revenue minus cost. Write an expression for the profit from making and selling x
units of the product.
21.
A 95% confidence interval for the mean gas mileage for a fleet of rental cars is from
17.42 to 22.58 miles per gallon. What was the sample average? Is it possible that the actual
average for the whole fleet is outside this interval?
22.
A battery manufacturer claims that the average life of its battery before recharging is at
least 40 hours. You think that is overly optimistic and so take a sample and conduct a hypothesis
test. Your p value is .206. What should you conclude?
Solutions
1.
.237 = 23.7%
2.
37.5% = .375
3.
5/7 = .7143 = 71.43%
In general, there is no need to carry your calculations beyond 4 decimal places.
Exceptions to this advice will be covered by your instructor.
4.
The percent is
52.37
 1.089  108.9%
48.09
Percent increase is
5.
(52.37  48.09) 4.28

 .089  8.9%
48.09
48.09
Values in order are
-5
-1.1 -1.01 -1
1
1.1
|-2| = 2
3
18
6.
One way to determine the arrangement is to convert all of these fractions to fractions with
the same denominator. The smallest common denominator (the smallest number that 2, 3, 6, and
8 all go into evenly) is 24.
1/2 = 12/24
1/3 = 8/24
5/6 = 20/24
3/8 = 9/24
In order, these values are 1/3, 3/8, 1/2, and 5/6.
An alternative way to determine the arrangement is to convert these all to decimals.
1/2 = .5
1/3 = .3333
5/6 = .8333
3/8 = .375
In order, these values are 1/3, 3/8, 1/2, and 5/6.
7.
5>3
-1.11 > -1.12
-5 < 3
-1.11 < -1.10
-5 < -3
8.
The order of operations is to work inside parentheses first. Do exponents, then
multiplication and division, then finally addition and subtraction.
2.6
(8  2.16) 2
5
2.6
 14.36 
(5.84) 2
5
2.6
 14.36 
(34.1056)
5
 14.36  .52(34.1056)
14.36 
 14.36  17.7349
 3.3749
9.
3
5(2  ) 2  5(3.5) 2  5(12.25)  61.25
2
10.
Price from Supplier A:
(1200 units)($4.00 / unit) = $4800.
Price from Supplier B:
(200 units)($6.00 / unit) + (500 units)($4.00 / unit) + (500 units)($3.00 / unit)
= $1200 + $2000 + $1500 = $4700.
Supplier B has the better price for 1200 units.
11.
a.
1/2 + 3/7 = 7/14 + 6/14 = 13/14
b.
(2)(3)( 4) 3

(5)(8)
5
c.
6(5 x  2)
 2(5 x  2)  10 x  4
3
d.
5 3 10 3 13




x 2x 2x 2x 2x
e.
(-5)2 = 25
f.
41 / 2  4  2
g.
4 1 / 2 
1
4
1/ 2

1
4

1
 .5
2
12.
The average is found by adding up all of the prices and dividing by 5000. The result will
always be a number somewhere between the largest and smallest values.
a.
5000 is the number of prices in the sample; it cannot be the average because it is
too large
b.
8.65 cannot be the average; it is smaller than the smallest value
c.
41.19 could be the average
d.
47.38 could only be the average if all 5000 prices were equal to this value; at least
one prescription was priced at $13.12.
e.
25.25 could be the average
f.
53.29 cannot be the average; it is larger than the largest value
Although 25.25 could be the average, its position midway between the largest and smallest
values doesn’t indicate that it should be the average.
13.
a.
5x – 3 = 12
5x = 15
x=3
b.
2x + 1 > x – 5
x + 1 > -5
x > -6
c.
4x + 2 < 7x – 4
2 < 3x – 4
6 < 3x
2<x
14.
(18 + 2(12))(1.07) = (18 + 24)(1.07) = 41(1.07) = 44.94
15.
y gets larger as x gets larger
16.
a.
b.
c.
d.
e.
f.
17.
the slope is 2 (the line increases by 2 units for every 1 unit it moves to the right)
18.
y = 2x + 2
19.
a.
b.
c.
d.
(-1, 0) is on the line
(-1, 2) is not on the line
(2, 0) is not on the line
(0, 2) is on the line
(1, 4) is on the line
(0, 0) is not on the line
 x = 4 + 3 + 5 + 1 + 2 = 15
 x = 16 + 9 + 25 + 1 + 4 = 55
 x  = (15)2 = 225
 xy = 4(1) + 3(2) + 5(0) + 1(6) + 2(5) = 26
2
2
e.
20.
 x y =15(1 + 2 + 0 + 6 + 5) = 15(14) = 210
Revenue = 300x
Cost = 200x + 10000
Profit = Revenue – Cost = 300x – (200x + 10000) = 100x – 10000
21.
The sample mean is the center of this confidence interval or 20. It is certainly possible
that the population mean lies outside this interval, but we have a strong degree of belief (95%)
that the population mean is between 17.42 and 22.58.
22.
Because the p value is larger than most customary values of alpha, we would not be able
to reject the manufacturer’s claim.