Download test two review problems

Mathematics 107 test two review problems
1. A price increases from $250 to $290. Calculate the percent increase.
2. The price of a house is reduced 10% to a new price of $360,000. What was the original
price?
3. A bond is purchased for $500 and is sold for $600 four years later. Assuming simple
interest, what is the annual percentage rate in this case?
4. Suppose the heights of 1000 people are normally distributed, with a mean height of 160
cm and a standard deviation of 20 cm.
• what percentage of the heights are within one standard deviation of the mean?
• how many heights are less than 130 cm ?
• what height corresponds to the 90th percentile?
5. In the year 2000, a house had a value
of $300,000. Every year the value of the
house increased by exactly 5%. What was
the house’s value in the year 2007?
6. The amount of money in a savings account
grows by exactly 3% each year. If the account
starts with $1000, when will the account contain more than $10,000 for the first time?
7. A company needs $10,000 in five years to
replace a piece of equipment. At the end of
each month, the company deposits money
into an account earning 6% A.P.R., compounded monthly. Calculate the amount of
each deposit. (assuming the deposit amounts are
8. A couple wants to deposit $1000 into an account today and have this amount grow to $
4000 in 15 years. What rate of interest, compounded once a year, will be necessary?
equal)
9. A 9% A.P.R. compounded monthly corresponds to what effective rate of interest?
10. A 25-year housing loan has an interest rate of 5% A.P.R., compounded monthly, and
monthly payments of $1200.
• calculate the amount of the loan
• how much interest is paid on this loan?
• how much is owed on the loan after making 15 years of payments?
11. A game pays out $300 to 1 in a thousand players, and $20 to 30 in 1000 players, while
the remaining players lose $1. What is the expected value of the winnings of a player at this
game ? To what value should the loss amount be changed to make the game fair ?
12. In a group of 85 people, 40 have jobs, 50 have cars, and 35 have both a job and a
car. If J represents the event “having a job” and C the event “having a car” compute the
probabilities
(a) P (J)
(b) P (J|C)
( conditional probability ! )
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13. There were 20 workers working at 3 different hourly wage levels at a small factory. The
data on their wages is presented below:
$ 35 , $ 35 , $ 35 , $ 35 , $ 35 ,
$12
20 , $ 20 , $ 20 , $ 20 , $ 20 , $ 20 , $ 20 ,
$11
10 , $ 10 , $ 10 , $ 10 , $ 10 , $ 10 , $ 10 , $ 10
(a)
10Sketch a bar graph and pie chart illustrating the data:
9
8
7
6
5
4
3
2
1
0
14. (refers to data in problem 13)
The mode hourly wage is
The median hourly wage is
The mean (or average) hourly wage is
15. (refers to data in problem 13)
The range of the hourly wages is
The standard deviation of the hourly wages is