Download 243_T_1_Review

Exam 1 Review
Math 243 – Probability and Statistics 1 – Bunnell
General
Exam 1 will cover chapter 1 and sections 2.1, 2.2, 3.1, 3.2, 3.4, 3.5, 4.1, 5.1, 5.2 and 5.3.
Calculators are necessary. To prepare for the exam you should review homework
assignments, book problems and the “Study Plan” section online.
Topics
This is a list of all general topics that have been covered so far this term. Make sure you are
comfortable with the terminology and problems associated with each topic.
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Statistics and Parameters
Types of Data
o Quantitative/Qualitative
o Levels of Measure
o Discrete/Continuous
Types of Sampling
Frequency Distributions
Histograms
o Class Width
o Lower and Upper Class Limits
Pie Charts
Scatter Diagrams (2 Variables)
Measures of Central Tendency
o Arithmetic Mean/Median/Mode
o Mean and Median in Skewed Data
Measures of Dispersion
o Range/Standard Deviation/Variance/Interquartile Range
Empirical Rule
Z-scores
Percentiles
Quartiles
o 5-Number Summary
Correlation
o Linear Correlation Coefficient
Probability
o Sample Space
o Events
o Properties of Probability P(E)
o Addition Rule
o Multiplication Rule
o Empirical/Subjective/Theoretical
Problems
The listed problems are similar to those you may see on the test. This list is not meant to
represent every type of problem you will see on the exam, so be sure to look at other
problems we have done this term. These problems are for your practice and will not be
collected or graded.
Part 1
1) Statistic or Parameter?
 In a survey conducted in the town of Atherton, 25% of adult respondents
reported that they had been involved in at least one car accident in the past
ten years.
 28.2% of the mayors of cities in a certain state are from minority groups.
 A study of 3700 college students in the city of Pemblington found that 8%
had been victims of violent crimes.
 51.5% of the residents of Idlington Garden City are female.
 Telephone interviews of 372 employees of a large electronics company found
that 65% were dissatisfied with their working conditions.
 The average age of the 65 students in Ms. Hopeʹs political science class is 21
years 7 months.
 Mark retired from competitive athletics last year. In his career as a sprinter
he had competed in the 100 –meters event a total of 328 times. His average
time for these 328 races was 10.25 seconds.
2) Quantitative or Qualitative?
 the number of seats in a school auditorium
 the numbers on the shirts of a boyʹs football team
 the bank account numbers of the students in a class
 the weights of cases loaded onto an airport conveyor belt
 the temperatures of cups of coffee served at a restaurant
 the native languages of students in an English class
3) Continuous or Discrete?
 the speed of a car on a Boston tollway during rush hour traffic
 the number of phone calls to the police department on any given day
 the age of the oldest employee in the data processing department
 the number of pills in an aspirin bottle
4) Level of Measurement?
 ranking (first place, second place, etc.) of contestants in a singing
competition
 capacity of a backpack
 an evaluation received by a physics student (excellent, good, satisfactory, or
poor).
 the year of manufacture of a car
 time spent playing basketball
 category of storm (gale, hurricane, etc.)
Part 2
5) Calculate the mean, median, and mode for the following sample:
5, 10, 6, 100, 0, 0, 10, 0
6) The high temperatures (in degrees Celsius) each day over a three week period were
as follows:
17, 18, 20, 22, 21, 19, 16, 15, 18, 20, 21, 21, 22, 21, 19, 20, 19, 17, 16, 16, 17
Compute the mean, median, and mode.
7) The number of yards that a football player rushed in the first 13 games of his NFL
career are listed below. Find the mean and median number of yards rushed. Round
the mean to the nearest whole number. Which measure of central tendency-the
mean or the median-better represents the data? Explain your reasoning.
3, 49, 32, 33, 39, 22, 42, 9, 9, 39, 52, 58, 70
8) The costs (in dollars) of 10 college math textbooks are listed below. Find the sample
standard deviation.
70 72 71 70 69 73 69 68 70 71
9) The January utility bills (in dollars) for 20 residents of a large city are listed below.
Find the range of the data.
70 72 71 70 69 73 69 68 70 71
67 71 70 74 69 68 71 71 71 72
10) The monthly telephone usage (in minutes) of 30 adults is listed below. Find the
interquartile range for the telephone usage of the 30 adults.
154 156 165 165 170 171 172 180 184 185
189 189 190 192 195 198 198 200 200 200
205 205 211 215 220 220 225 238 255 265
Part 3
11) A small computing center has found that the number of jobs submitted per day to its
computers has a distribution that is approximately bell shaped, with a mean of 84
jobs and a standard deviation of 10. Where do we expect most (approximately 95%)
of the distribution to fall?
12) A study was designed to investigate the effects of two variables - (1) a studentʹs
level of mathematical anxiety and (2) teaching method - on a studentʹs achievement
in a mathematics course. Students who had a low level of mathematical anxiety
were taught using the traditional expository method. These students obtained a
mean score of 460 with a standard deviation of 50 on a standardized test. Assuming
a bell-shaped distribution, what percentage of scores exceeded 360?
13) Find the z-score of 532 if 𝜇 = 623 and 𝜎 = 64.
14) The percentage of measurements that are above the 39th percentile is _________.
Part 4
15) Identify the sample space of the probability experiments.
 tossing a coin
 answering a true or false question
 tossing four coins and recording the number of heads
16) What is the probability of flipping a coin 5 times and getting at least 1 heads?
17) Which of the following cannot be the probability of an event?
-0.04
√7
3
0
5
0.945
18) The bar graph shows the number of tickets sold each week by the garden club for their
annual flower show.
Number of Tickets Sold
60
50
40
30
20
10
0
1
2
3
4
5
6
Week
a. During which week were the most number of tickets sold?
b. During which week were the fewest number of tickets sold?
c. How many tickets were sold during week 5?
19) Approximate the correlation coefficient 𝑟 for the following scatter diagram.