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.
· 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 0 73 5 0.945
18) The bar graph shows the number of tickets sold each week by the garden club for their annual flower show.
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.