Review Problems for Exam II
1.
2.
Which of the relative frequency histograms below represents data that is (approximately) normally
distributed?
a)
b)
c)
d)
Two hundred and fifty students take a college entrance exam. The scores on the exam have an
approximately normal distribution with mean 52 points and the standard deviation 11 points.
a)
b)
c)
d)
e)
d)
3.
Estimate the average score on the exam.
Estimate what percent of the students scored 52 points or more.
Estimate what percent of the students scored between 41 and 63 points.
Estimate what percent of the students scored 63 points or more.
Estimate what percent of the students scored between 30 and 74 points.
Estimate what percent of the students scored between 19 and 85 points.
Suppose you take an exam with 400 possible points. The instructor tells you that the test scores were
normally distributed with a mean score of 280 and standard deviation of 35. You got a 315. In what
percentile did you score?
4.
In California, school bond measures require a 66.67% vote for approval. Suppose that an important
school bond measure is on the ballot in the upcoming election. In the most recent poll conducted, 70%
of the voters say that they will vote for the school bond measure and at the 95% confidence level, the
margin of error is 4%. Can we conclude that the school bond measure will pass? Explain.
5.
The Food and Nutrition Board of the National Academy of Sciences states that the RDA of iron for
adult females under the age of 51 is 18mg. A sample of 100 adult females under the age of 51 found
that the mean daily intake of iron for women in the sample was 14.7 mg. The Food and Nutrition
board has calculated that if adult women do, on average, get the required 18 mg of iron, the chances of
a randomly chosen sample of 100 having a mean intake of iron being 14.7 is approximately 1 in 200.
Is this result statistically significant at the .01 level? Would it be reasonable for the Food and
Nutrition Board to conclude that, on average, females under the age of 51 are getting less that the
RDA of 18 mg of iron?
6.
A September 2008 poll conducted by the Field Corporation surveyed 830 likely voters in
California regarding Proposition 3, the Children's Hospital Bond initiative.. Of those surveyed,
47% said they intend to vote Yes, while 35% said they intend to vote No. However, 18% of those
surveyed said they were undecided. What is the margin of error and a 95% confidence interval for
these results? Interpret these results. Would you expect Proposition 3 to pass?
7.
An amount of $2,500 is deposited in a bank that pays interest at the rate of 7% per year, compounded
daily. What is the total amount in the account at the end of six years, assuming there are no deposits or
withdrawals during those six years?
8.
Find how much money should be deposited in a bank paying interest at the rate of 8.5% per year
compounded quarterly so that at the end of five years, the accumulated amount will be $40,000.
9.
As a savings program toward their child’s college education, the parents decide to deposit $100 at the
end of every month into a time-deposit bank account paying interest at the rate of 6% per year
compounded monthly. If the savings program began when the child was 6 years old, how much
money would have accumulated by the time the child turns 18?
10.
The Pirerra’s are planning to go to Europe three years from now and believe they will need $8,000 for
the trip. They have now agreed to put a certain amount into a savings account each month in order to
save for the trip. How much money do they need to deposit each month into an account that pays
6.5% compounded monthly in order to have the $8,000 in savings three years from now?
11.
Find the annual percentage yield on a savings account with 6.9% interest compounded monthly.
12. You just received a $950 bill for your credit card, which has an annual interest rate of 18%. Your credit
card company charges interest on the unpaid balance in order to calculate the interest you owe. Suppose
you make a $150 payment now, and make no new charges to your credit card in the next month. What
will be the balance on your next credit card bill (a month from now)?
13. You just received an $800 bill for your credit card, which has an annual interest rate of 21%. Your credit
card company charges interest on the unpaid balance in order to calculate the interest you owe. Suppose
you make a $200 payment now, and make $100 in new charges to your credit card in the next month.
What will be the balance on your next credit card bill (a month from now)?
14. You just received a $500 bill for your credit card, which has an annual interest rate of 21%. Your credit
card company charges interest on the unpaid balance on the first day of the billing period in order to
calculate the interest you owe. Suppose you make a $100 payment next week, and make no new charges
to your credit card in the next month. What will be the balance on your next credit card bill (a month from
now)?
15. You just received a $1,000 bill for your credit card, which has an annual interest rate of 18%. Your credit
card company charges interest on the unpaid balance on the first day of the billing period in order to
calculate the interest you owe. Suppose you make a $200 payment tomorrow, and make no new charges
to your credit card in the next month. What will be the balance on your next credit card bill (a month from
now)?
16. Compute the total return and the annual return for each of the following investments.
a) Seven years after buying 100 shares of ABC stock for $27 per share, you sell all of your shares for
$3400.
b) You purchase a municipal bond for $5000. The bond matures in 10 years, at which time you receive
$7500.
c) Ten years after purchasing shares in a mutual fund for $5000, you sell them for $8600.
d) Seven years after paying $3000 for shares in a new company, you sell the shares for $1000.
18. The Jacksons have determined that after making a down payment they could afford at most $1,000 for a
monthly house payment. If the bank’s annual interest rate is 10.5%, and the loan is a 30 year loan, what is
the maximum amount that the Jacksons can borrow from the bank?
19. The price of a new car is $8,000. If you make a down payment of 25% toward the purchase of the car and
secure financing for the balance at the annual interest rate of 10%
a) what will your monthly payment be if the car is financed over a period of 36 months? Over a period
of 48 months?
b) What will the interest charges be if you elect the 36-month plan? The 48-month plan?
20. Mr. Fletcher opened an IRA account on January 31, 1980 with a $3,500 deposit. He made not
additional deposits, until January 31, 1985, when he began to make $1,500 deposits each January 31
until January 31, 2008. How much will be in the account on January 31, 2008 if the account earns
7% interest compounded annually?
Answers
1.
2.
3.
4.
a) and d) are normally distributed, b) and c) are not.
a) 52
b) 50%
c) 68%
d) 16%
e) 95%
f) 99.7%
th
about the 89 percentile.
No. The confidence interval obtained is 66% -74%. Not all values in this interval represent a situation
in which the school bond will pass; so we cannot conclude that it will pass.
5. Yes it is statistically significant at the .01 level since the probability that the difference occurred by
chance is 1/200 = .005 < .01. The Food and Nutrition Board should conclude that the difference did not
occur by chance, and so adult women under the age of 51, on the average, do not intake enough iron.
6. The margin of error is about 3.5%; a 95% confidence interval for the percent of all likely voters in
California that would vote yes on Prop. 3 was between 43.5% and 50.5%. Interpretation: there is a 95%
chance that the actual percent of all likely voters in California that would vote yes on Prop. 3 was
between 43.5% and 50.5%. A similar confidence interval and interpretation can be given for the percent
of all likely voters in California that would vote no on Prop. 3.
7.
12.
15.
18.
$3,804.75
$812.00
$815.00
$109,321.
16.
8. $26,267.49
9. $21,015.02
10. $201.86
11. 7.14%
13. $710.50
14. $408.75
a) 25.9%; 3.3%
b) 50%; 4.1%
c) 72%; 5.6% d) – 66.7%; –14.5%
19. a) $193.60; $152.18
b) $969.60; $1304.64.
20. $103,425.14