College Prep Stats
REVIEW for MIDTERM EXAM
Name ______________________________
For all probability answers, round to three decimal places.
1. Determine whether the given value is a statistic or a parameter. A health and fitness club surveys 40 randomly selected members
and found that the average weight of those questioned is 157 lb.
2. Determine whether the given value is from a discrete or continuous data set.
a) The number of freshmen entering college in a certain year is 621.
b) The temperature of a cup of coffee is 67.3°F.
3. Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate.
a) Salaries of college professors.
b) Temperatures of the ocean at various depths.
4. Identify which of these types of sampling is used: random, stratified, systematic, cluster, convenience.
a) An education researcher randomly selects 48 middle schools and interviews all the teachers at each school.
b) A tax auditor selects every 1000th income tax return that is received.
c) 49, 34, and 48 students are selected from the Sophomore, Junior, and Senior classes with 496, 348, and 481 students respectively.
5. a) Alex and Juana went on a 100-mile canoe trip with their class. On the first day they traveled 26 miles. What percent of the total
distance did they canoe?
b) On a test, if 80 questions are answered and 76 of them are correct, what is the percent of correct answers? Round to the nearest
percent.
c) On a test, 55% of the questions are answered correctly. If 44 questions are correct, how many questions are on the test?
d) A lawyer has 40 clients, 10% of whom are businesses. Find the number of business clients.
6. Use common sense to determine whether the given event is impossible; possible, but very unlikely; or possible and likely.
a) An accountant was struck by lightning three times in his lifetime.
b) The ten participants of a seminar on public speaking all showed up on time.
Use the following frequency distribution to answer numbers 7 – 12: Days off
0–2
7. What is the class width?
3–5
6–8
8. What is the class midpoint of the 9 – 11 class?
9 – 11
12 – 14
9. What are the class boundaries for the 15 – 17 class?
15 – 17
10. What is the lower limit of the 6 – 8 class?
11. Create the cumulative frequency distribution.
12. Create the relative frequency distribution.
Frequency
10
1
7
7
1
4
13. The pie chart shows the percent of the total population of 73,700 of Springfield living in the given types of housing.
a) Find the number of people who live in condos.
b) Find the number of people who live in townhouses.
Use the following data for numbers 14 – 20:
1 5 7 8 12 16 18 25 57 90 99 126 136 167
14. Find the mean.
15. Find the standard deviation.
16. Find the coefficient of variation.
17. a) Determine the z-score for 12.
b) Determine the z-score for 99.
18. a) Find P29.
b) Find P61.
19. What percentile is 99?
20. Does this data contain any outliers?
Please round all probability answers to the thousandths place.
21. Between what two values does a probability lie?
22. Determine whether the events are disjoint:
a) Go to a formal dinner affair.
Wear blue jeans.
b) Draw one ball colored red from a bag.
Draw one ball colored blue from the same bag.
1
23. a) If P(A) = , find P  A  .
7
b) Based on meteorological records, the probability that it will snow in a certain town on January 1st is 0.185. Find the probability
that in a given year it will not snow on January 1st in that town.
c) If a person is randomly selected, find the probability that his or her birthday is not in May. Ignore leap years.
24. a) Refer to the table which summarizes the results of testing for a certain disease. If one of the results is randomly selected, what
is the probability that it is a false negative (test indicates the person does not have the disease when in fact they do)?
Subject has the disease
Subject does not have the disease
Positive Test Result
120
13
Negative Test Result
4
172
b) The table below describes the smoking habits of a group of asthma sufferers. If one of the 1197 people is randomly selected, find
the probability of getting a regular or heavy smoker.
Nonsmoker
Men
Women
Total
444
429
873
Occasional
smoker
37
47
84
Regular
smoker
76
86
162
Heavy
smoker
34
44
78
Total
591
606
1197
25. a) Find the probability of correctly answering the first 5 questions on a multiple choice test if random guesses are made and each
question has 6 possible answers.
b) You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the probability that the
first card is a King and the second card is a queen. Express your answer as a simplified fraction.
26. a) A sample of 100 wood and 100 graphite tennis rackets are taken from the warehouse. If 6 wood and 14 graphite are defective
and one racket is randomly selected from the sample, find the probability that the racket is wood or defective.
b) 100 employees of a company are asked how they get to work and whether they work full time or part time. The figure below shows
the results. If one of the 100 employees is randomly selected, find the probability of getting someone who carpools or someone who
works full time.
1. Public transportation: 7 full time, 10 part time
2. Bicycle: 4 full time, 3 part time
3. Drive alone: 30 full time, 31 part time
4. Carpool: 6 full time, 9 part time
27. From the information provided, create the sample space of possible outcomes.
a) Friskie is having her fifth litter. The prior litters have either been three normal pups or two normal pups and a runt. Assume the
probability of either outcome is 50%.
b) Two white mice mate. The male has both a white and a black fur-color gene. The female has only white fur-color genes. The fur
color of the offspring depends on the pairs of fur-color genes that they receive. Assume that neither the white nor the black gene
dominates.
28. a) An unprepared student makes random guesses for the ten true-false questions on a quiz. Find the probability that there is at
least one correct answer.
b) In a batch of 8,000 clock radios 5% are defective. A sample of 14 clock radios is randomly selected without replacement from the
8,000 and tested. The entire batch will be rejected if at least one of those tested is defective. What is the probability that the entire
batch will be rejected?
29. Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find
the probability of x successes given the probability p of success on a single trial.
a) n = 30, x = 12, p = 0.20
b) n = 6, x = 3, p =
1
6
c) n =12, x = 5, p = 0.25
30. Determine whether the given procedure results in a binomial distribution. If not, explain why.
a) Choosing 5 people (without replacement) from a group of 58 people, of which 15 are women, keeping track of the number of men
chosen.
b) Rolling a single "loaded" die 50 times, keeping track of the "fives" rolled.
c) Choosing 10 marbles from a box of 40 marbles (20 purple, 12 red, and 8 green) one at a time with replacement, keeping track of the
number of red marbles chosen.
31. Find the mean of the given probability distribution.
x
3
6
9
12
15
P(x)
0.14
0.05
0.36
0.35
0.10
32. Find the mean, μ, for the binomial distribution which has the stated values of n and p.
a) n = 44; p = 0.2
b) n = 1632; p = 0.57
c) n = 2772; p = 0.63
33. Find the standard deviation, σ, for the binomial distribution which has the stated values of n and p.
a) n = 38; p = 0.6
b) n = 2165; p = 0.63
c) n = 47; p = 0.4
34. Assume that a researcher randomly selects 14 newborn babies and counts the number of girls selected, x. The probabilities
corresponding to the 14 possible values of x are summarized in the given table. Answer the question using the table.
a) Find the probability of selecting 12 or more girls.
b) Find the probability of selecting 9 or more girls.
c) Find the probability of selecting exactly 5 girls.
x (girls)
0
1
2
3
4
P(x)
0.000
0.001
0.006
0.022
0.061
Probabilities of Girls
x (girls)
P(x)
5
0.122
6
0.183
7
0.209
8
0.183
9
0.122
x (girls)
10
11
12
13
14
P(x)
0.061
0.022
0.006
0.002
0.000
35. In a study of headache patients, every one of the study subjects with a headache was found to be improved after taking a week off
of work. Can we conclude that taking time off work cures headaches?
36. Give an example of a quantitative variable.
37. Identify the sample: An employee at the local ice cream parlor asks three customers if they like chocolate ice cream.
38. Identify the population: An employee at the local ice cream parlor asks three customers if they like chocolate ice cream.
Use the following information for numbers 39 – 43:
Below is some information about films nominated for the “Best Movie” Academy Award (Oscar) in 2009. Here is a pie chart for the
distribution of the variable “Genre.” Fill in the blanks with the appropriate percentages.
39. ______
Name
Avatar
The Blind Side
District 9
An Education
The Hurt Locker
Inglorious Basterds
Precious
A Serious Man
Up
Up in the Air
Genre
Adventure
Drama
Action
Drama
Action
Drama
Drama
Comedy
Animated
Comedy
MMPA Rating
PG-13
PG-13
R
PG-13
R
R
R
R
PG
R
43. ______
Action
Drama
Comedy
42. ______
44. Using the empirical rule, what percent of data lie within 1 standard deviations of the mean?
45. List all the measure of center that are non- resistant.
40. ______
41. ______