Download statistics final exam topics and review

STATISTICS FINAL EXAM REVIEW
The final will consist of chapters 4, 5, 6, and 9. Please do the following review problems.
Look over all notes, packets, homework, quizzes, and tests, in addition to the review problems
to properly study for the exam. Make sure you bring a pencil and graphing calculator to the
exam. Also, a z-score sheet, t-score sheet, and formula sheet will be provided. Good luck!!
Senior Exam Date:_________________________________
Underclassman Exam Date:__________________________
Chapter 4: (4.1 – 4.3)
Discrete or continuous?
1. x is the length of time students take to walk to school.
2. x is the number of times the Yankees have won this season.
3. What are the two conditions for a probability distribution?
4.
x
P(x)
0
0.42
1
0.09
2
3
0.33
Find the missing value in the probability distribution.
5. Students take a quick quiz with 4 questions. The x number of questions
answered correctly is shown below in the chart.
Questions
# of times answered
correctly
1
2
3
4
10
8
12
20
Construct a chart to find the mean, variance and standard deviation. Then
interpret the results. (Round only at the standard deviation to the hundredth)
6. At a stats party, there were 100 tickets sold with five prizes raffled off:
$300, $200, $200, $100, $50. You buy one ticket for $5. What is the
expected value of your gain? (round to the hundredth)
7. How do you know if a distribution is binomial?
8. 100 people who were surveyed about the most annoying habit of drivers.
29% said that road rage was the most annoying habit. You randomly select
6 people who participated in the survey and ask if road rage is the most
annoying habit.
a) Find n, p, q, x.
b) Construct a binomial distribution for the probabilities.
c) Find the probability of exactly 4 choosing road rage.
d) Find the probability of at least 3 choosing road rage.
e) Find the probability of less than 3 choosing road rage.
g) Find the mean, variance, and standard deviation.
h) Interpret the results.
9. Basketball player Shaquille O’Neal makes a free-throw shot about 53% of
the time. Find following probabilities by geometric distribution. Round to the
thousandth.
a) He makes his first basket on his second shot.
b) He makes his first basket on the first, second,
or third shot.
10. The mean bankruptcies filed per minute in the US in a recent year is 3.
Find the following probabilities by poisson distribution. Round to the
thousandth.
a) Exactly four businesses will file bankruptcy.
b) At most four businesses will file bankruptcy.
c) More than four businesses will file bankruptcy.
Chapter 5: (5.1 – 5.5)
1. Describe the similarities and differences of the two normal curves.
2. Construct a normal distribution with a mean of 25 and a standard
deviation of 3. (empirical rule)
Use #2 for the next questions (3-7)
3. What are the inflection points
4. What is the area under the curve between 22 and 31?
5. What is the area under the curve between 16 and 28?
6. Find the z-scores if the mean is 3 and the standard deviation is .02.
a) x = 3
b) x = 2.97
c) x = 3.05
7. Find the x-values if the mean is 15 and the standard deviation is 2.
a) z = 1.4
b) z = -2.35
c) z = 0
8. Find the area:
a) Left of z = 2.03
b) Right of z = -1.45
a) Left of z = - 1.285
d) Between z = 0 and z = 1.65
e) Left of z = -2.5 or right of z = 1.94
9. Find the z-score that is in the 58th percentile.
f) P(-.89 < z < 0)
10. In a recent year, the ACT scores for high school students were
normally distributed for students with a B to A average. The mean was
24.2 with a standard deviation of 4.3.
a) Find the probability that the student’s ACT score is less than 17.
b) Find the probability that the student’s ACT score is between 20 and
29.
c) Find the probability that the student’s ACT score is more than 32.
d) If 500 students with B to A averages were randomly selected, how
many would score more than 32?
11. The annual per capita consumption of ice cream(in pounds) in the US
is normal distributed with a mean of 15.4 lbs and a standard deviation of
2.5 lbs.
a) What is the maximum consumption of ice cream that can be in the
lowest 15%?
b) What is the minimum consumption of ice cream that can be in the top
25%?
12. SAT scores have a mean of 1000 and a standard deviation of 200.
ACT scores have a mean of 22 and a standard deviation of 5. If you
scored a 28 on the ACT and 1350 on the SAT, which test did you score
better? What percentiles were you in for SAT and ACT? (Assume SAT and
ACT tests are normally distributed
The population mean annual salary for registered nurses is $28,000 with a
standard deviation of $4,700. A sample of 35 registered nurses is randomly
selected.
13. What is the probability that the mean annual salary of the sample is less
than $29,500?
14. What is the probability that the mean annual salary of the sample is
between $26,000 and $30,000?
15. What is the probability that the mean annual salary of the sample is
more than $27,500?
Use for #16-18. A binomial experiment is given. Decide whether you can
use the normal distribution to approximate the binomial distribution. If so,
find the mean and standard deviation. If not, explain why.
16.In a recent year, the American Cancer Society predicted that the fiveyear survival rate for new cases of kidney cancer would be 59%. You
randomly select 12 men who were new kidney cancer cases and calculate
their survival rate.
17. A survey found that 46% of women who take at least one vacation a
year pack too much. You randomly select 12 women who take at least
one vacation a year and ask them if they pack too much.
18. A survey found that 94% of this class wants to learn more! You
randomly select 6 people to see if they are interested in learning more.
Find the probabilities.
19. Sixty-five percent of children aged 12 – 17 keep their savings in a
savings account. You randomly select 45 children and ask each if he or
she keeps his or her savings in a savings account.
a) Find the probability at most 20 children say yes.
b) Find the probability at least 35 children say yes.
c)
Find the probability that exactly 25 children say yes.
Chapter 6: (6.1 – 6.2)
For #1-4, decide if you would use a normal distribution, t-distribution, or
neither. Do not solve!
1) For a sample of 20 IQ scores the mean score is 105.8. The standard
deviation, σ, is 15. Assume that IQ scores are normally distributed.
2) In a random sample of 28 families, the average weekly food expense was
$95.60. Assume the distribution of weekly food expenses is not normally
distributed.
3)A random sample of 15 statistics textbooks has a mean price of $105 with
a standard deviation of $30.25. Assume the distribution of statistics textbook
prices is normally distributed.
4) A random sample of 35 people has an average age of 22 with a standard
deviation of 2.5 years.
Solve.
5)Find the critical value z c that corresponds to a 94% confidence level.
6)A random sample of 150 students has a grade point average with a mean
of 2.86 and with a standard deviation of 0.78. Construct the confidence
interval, if c = 0.98.
7)Find the critical value, t c for c = 0.99 and n = 10.
8)Construct a 90% confidence interval for the population mean, μ. Assume
the population has a normal distribution. In a recent study of 22 eighth
graders, the mean number of hours per week that they watched television
was 19.6 with a sample standard deviation of 5.8 hours.
9)A random sample of 10 parking meters in a beach community showed the
following incomes for a day. Assume the incomes are normally distributed.
$3.60 $4.50 $2.80 $6.30 $2.60 $5.20 $6.75 $4.25 $8.00 $3.00
Find the 95% confidence interval and interpret the results.
Chapter 9: (9.1 – 9.3)
The annual per capita sugar consumption (in kilograms) and the average
number of cavities of 11-12 year old children in seven countries.
SUGARCAVITIES-
2.1
.59
5.0
1.51
6.3
1.55
6.5
1.70
7.7
2.18
8.7
2.10
11.6
2.43
1.
Determine which is the independent (explanatory) and dependent
(response) variable.
2.
Which goes on the x-axis and on the y-axis?
3.
Graph on the calculator.
Directions: Put data in L1 and L2. Press 2nd and y= make sure your
scatter plot is turned on. Press zoom 9.
4.
By only looking at the graph, is the correlation positive, negative or
is there none? How do you know?
5.
Using the calculator, find the correlation coefficient ( r ).
Directions: Press stat calc 4 L1, L2 enter
6.
What is the correlation now using the correlation coefficient? Why?
7.
Write the prediction equation in slope-intercept form. Round the
decimals to the nearest thousandth.
8.
Plot the prediction equation on your graphing calculator.
Directions: Press y= and clear anything there.
Press vars 5 eq enter graph
9.
If a person had a sugar consumption of 20.5, what would be the
number of cavities? Directions: Use the tableset and table buttons
for predictions or substitute into your prediction equation.
10.
If a person had 5.2 cavities per year, what would be the sugar
consumption?
Use the tableset and table buttons for predictions or substitute into
your prediction equation.
11.
Find the correlation of determination (r²). Describe what this
number means.
12.
Construct a table to find the standard error of estimate. Round to
the nearest thousandth.