ST 371 Practice Test Flashcards

0.0(0)
studied byStudied by 5 people
learnLearn
examPractice Test
spaced repetitionSpaced Repetition
heart puzzleMatch
flashcardsFlashcards
Card Sorting

1/117

flashcard set

Earn XP

Description and Tags

Using all questions from quizzes and Exams

Study Analytics
Name
Mastery
Learn
Test
Matching
Spaced

No study sessions yet.

118 Terms

1
New cards
A Paramter is a numerical descriptive measure calculated from a sample T/F?
False
2
New cards
Our population of interest is NCSU students. The averag I.Q. of all NCSU students is called a statistic T/F?
False
3
New cards
A sociologist wishes to estimate the proportion of all adults in a certain region who have never married. In a random sample of 1,320 adults, 145 have never married. The Statistics involved is 0.1 T/F?
True
4
New cards
Martial status of a person is an example of quantitative - discrete data T/F?
False
5
New cards
Pie or Circle chart is not an appropriate graph for describing quantitative data T/F?
True
6
New cards
Stem-and-leaf plot provides the most infromation abotu the shape of a data set T/F?
True
7
New cards
Among 300 fatal car accidents, 135 were single-car crashes, 66 were two-car crashes, and 99 involved three or more cars. The relative frequency of fatal car accidents associated with two car crashes is 0.22 T/F?
True
8
New cards
The mean is much larger than the median would indicate that a dataset is skewed to the right T/F?
True
9
New cards
Median is NOT a meaure of spread T/F?
True
10
New cards
If an exam was worth 100 points, and your score was at the 80th percentile, then 20% of the class had scores at or below your score T/F?
False
11
New cards
Two or more events are said to be equally likely if each has got an equal chance for occurrence T/F?
True
12
New cards
The sample space denoted by the letter S is the set of a few possible outcomes of an experiment T/F?
False
13
New cards
What is an individual outcome in a sample space called?
A simple event
14
New cards
Happening and not happening of any event is always disjoint (Mutually Exclusive) T/F?
True
15
New cards
1\.01 is the number could be the probabilty of an event that is almost certain to occur T/F?
False because you cannot have 101% for statistics, only 100%.
16
New cards
Probability of happening and not happening of any event is always equal to zero T/F?
True
17
New cards
In any (fair/unfair) coin tossing experiement, probabilty of getting a head or tail is always equal to 0.5 T/F?
False
18
New cards
If E1 and E2 are two events, then union probability is denoted by P(E1 ∪ E2) and it is the probability that event E1 will occur or that event E2 will occur or both event E1 and event E2 will occur. T/F?
True
19
New cards
Joint probability of two events E1 and E2 is the probability of occurrence of event E1 or event E2. T/F?
False
20
New cards
Conditional probability of two events E1 given E2 is the probability of occurrence of event E1 given that event E2 has not already occurred. T/F?
False
21
New cards
SCENARIO 1: Questions 21 to 27 based on this scenario.

The data below represent the amount of grams of carbohydrates in a serving of

breakfast cereal in a sample of 11 different servings. (You can use R Software)

11        15        23        29        19        22        21        20        15        25        17

\
1\. Referring to Scenario 1, the range in the carbohydrate amounts is ________ grams.

a) 15 b) 5.10 c) 26.02 d)18
18
22
New cards
Referring to Scenario 1, the variance of the carbohydrate amounts is ________ (grams squared).

a) 5.10 b) 18 c) 15 d) 26.02
26\.02
23
New cards
Referring to Scenario 1, the standard deviation of the carbohydrate amounts is ________ grams.

a) 18 b) 5.10 c) 26.02 d) 15
5\.10
24
New cards
Referring to Scenario 1, the first quartile of the carbohydrate amounts is ________ grams.

a) 18 b) 5.10 c) 15 d) 26.02
15
25
New cards
Referring to Scenario 1, the third quartile of the carbohydrate amounts is ________ grams.

a) 15 b) 5.10 c) 23 d) 26.02
23
26
New cards
Referring to Scenario 1, the interquartile range in the carbohydrate amounts is ________ grams.

a) 15 b) 18 c) 8 d) 23
8
27
New cards
Referring to Scenario 1, the extreme values in the given data set are.

a) 25, 27 b) 11, 15 c) None of these d) 27 e) 11
None of These
28
New cards
SCENARIO 2: The mean price of new homes from a sample of houses is $150, 000 with a standard deviation of $15, 000. The data set has a bell-shaped distribution.

Referring to Scenario 2, Between what two prices do 95% of the new homes fall?
\
$120, 000 and $180, 000
29
New cards
Referring to Scenario 2, Find the approximate percentage of new homes whose prices are less than $135, 000?
16%
30
New cards
Referring to Scenario 2, Find the approximate percentage of new homes whose prices are greater than $165, 000?
16%
31
New cards
An experiment consists of tossing 4 unbiased coins simultaneously. The number of simple events in this experiment is
16
32
New cards
Question 32 – 39: Find the indicated probability

A sample space consists of 80 simple events that are equally likely. What is the probability of each?
1/80
33
New cards
A die with 12 sides is rolled. What is the probability of rolling a number less than 11?
5/6
34
New cards
A bag contains 6 red marbles, 3 blue marbles, and 7 green marbles. If a marble is randomly selected from the bag, what is the probability that it is blue?
3/16
35
New cards
A 6-sided die is rolled. What is the probability of rolling a 3 or a 6?
1/3
36
New cards
If P(A) = 12/19, find P(A^c). 
7/19
37
New cards
Based on meteorological records, the probability that it will snow in a certain town on January 1st is 0.315. Find the probability that in a given year it will not snow on January 1st in that town.
0\.685
38
New cards
In one town, 30% of all voters are Democrats. If two voters are randomly selected for a survey, find the probability that they are both Democrats
0\.09
39
New cards
A manufacturing process has a 70% yield, meaning that 70% of the products are acceptable and 30% are defective. If three of the products are randomly selected, find the probability that all of them are acceptable.
0\.343
40
New cards
A random variable cannot be both discrete and continuous T/F?
True
41
New cards
The number of letters in a word picked at random out of the dictionary is an example of continuous random variable. T/F?
False
42
New cards
The time (in seconds) it takes one email to travel between a sender and receiver is an example of continuous random variable. T/F?
True
43
New cards
The expected value for a random variable is the long – run average T/F?
True
44
New cards
In a Binomial Probability Distribution, each trial is dependent of every other trial. T/F?
False
45
New cards
Suppose that a random variable X can take the values {0, 1, 2} all with equal probability. Then the expected value of X is 1. T/F ?
True
46
New cards
Suppose each shell sells for $5.00. On average, Sai sells 1.5 shells per day. However, Sai must pay $3.00 daily for the permit to sell shells. Let Y denote Sai’s daily profit. Then Y=5X-3. Then E(Y) is $4.50. T/F?
True
47
New cards
If g(X) = 2X-5 is a linear combination of a random variable X, then  Var(2X-5) = 2Var(X). T/F?
False
48
New cards
Let X be the number of heads obtained in 40 independent tosses of a fair coin. Then X is a Binomial random variable with n=40, p=0.5. T/F?
True
49
New cards
Suppose that you toss a fair coin with probability 0.5 a head. The probability of getting five heads in a row is less than three percent. T/F?
False
50
New cards
Suppose that you toss a coin 5 times. Then there are 10 ways of getting 3 heads. T/F?
True
51
New cards
The probability of observing three heads out of five tosses of a fair coin is 0.6. T/F?
False
52
New cards
The probability of at least one head when tossing a fair coin 4 times is 0.9375. T/F?
True
53
New cards
Suppose that X is Binomially distributed with E(X) = 5 and Var(X) = 2, then n = 10 and p = 0.5. T/F?
False
54
New cards
A grocery store has 10 loaves of bread on its shelves, of which 7 are fresh and 3 are stale. Customers buy 4 loaves selecting them at random. The probability that 3 are fresh and 1 is stale is 0.5 T/F?
True
55
New cards
At Meet the Firms, a recruiter is interviewing candidates for an internship. From past experience, the recruiter believes that only about 20% of the potential candidates have the necessary qualifications. Assume independence. The probability that the first suitable job candidate will be found during the fourth interview is 0.1024 T/F?
True
56
New cards
An experiment consists of repeatedly and independently tossing a fair die until a six is obtained. Let X denote the number of throws before obtaining a six. Then E(X) =5 T/F?
True
57
New cards
A large collection of tires has 3% defective tires. Suppose one chooses tires from this collection until he/she obtains 4 non-defective tires. Then the total number of defective tires drawn in this process has a Negative Binomial distribution with r = 4, p = 0.03. T/F?
False
58
New cards
**Let X have a Poisson distribution with variance of 3. Then P(X=2) is 0.224 T/F?**
True
59
New cards
The number of typos made by a student follows Poisson distribution with the rate of 1.5 typos per page. Assume that the numbers of typos on different pages are independent. The probability that there are exactly 10 typos in a 5-page paper is 0.086 T/F?
True
60
New cards
SCENARIO 1: Questions 1 to 3 based on this scenario.

According to the October 2003 Current Population Survey, the following table summarizes probabilities for randomly selecting a full-time student in various age groups:

Age                     15-17            18-24         25-34            35 or older

Probability        .009                 .623           .210                .158

If we randomly select a full-time student, what is the probability that he/she is 25 or older?
0\.368
61
New cards
If we randomly select a full-time student, the probability that he/she is not 18-24 years old is
0\.377
62
New cards
If we randomly select a full-time student, the probability that he/she is 18-30 years old is
Impossible to determine from information provided
63
New cards
You pay $6 to play a game in which you roll a fair die. If you roll a 6, you get $8. If you roll a 5, you get $7. For any other number, you get $4. What are your expected net winnings?
\-$0.83
64
New cards
The probability that a person who has made a reservation for a trip on a twelve-vehicle ferry will actually, arrive and make the trip is 0.85. If to account for “no-shows” the ferry company makes 13 reservations for a particular trip, the chance that all 13 vehicles will show is about
0\.12
65
New cards
A trailer manufacturing company buys screw fasteners in boxes of 5,000. Two percent of all fasteners are unusable. The mean and standard deviation of the number x of unusable fasteners in a randomly selected box are about
(100, 9.9)
66
New cards
Forty percent of passengers with a certain airline prefer a window seat. The probability that exactly two of the next ten person buying a ticket with this airline will prefer a window seat is about:
0\.12
67
New cards
Suppose that a poll of 18 voters is taken in a large city. The random variable x denotes the number of voters who favor a certain candidate for mayor. Suppose that 61% of all the city’s voters favor the candidate. The mean and standard deviation of x are respectively
(10.98, 2.07)
68
New cards
If X \~ Bin(n=15, p=1/3). Find the probability P(mu - sigma < X < mu + sigma)
0\.58772
69
New cards
One in five $1 lottery tickets wins the buyer some kind of payoff. If a person buys five tickets, the probability that none will be a winning ticket is about:
0\.33
70
New cards
Consider a random variable Y with the probability density function

fY(y)=|y|/k,−1
5
71
New cards
Consider a random variable X with the probability density function

fX(x)={1/10+1/5x,for1≤x≤3

The CDF of X is
(x^2 + x -2) / 10
72
New cards
Consider a random variable X with the probability density function

fX(x)={1/10+1/5x, for1≤x≤3,

The expected value of of X is
2\.133
73
New cards
The probability distribution (pdf) of a random variable X is:

fX(x)={3/2(1−x^2), for0≤x≤1

Determine the mean of X, E(X) is
0\.375
74
New cards
The probability distribution (pdf) of a random variable X is:

fX(x)={3/2(1−x^2), for0≤x≤1

Determine the E(X2).
0\.2
75
New cards
Suppose the density of X is  \n fX(x)={3x^2, for0≤x≤1 \n Find a median value of X.
1/(3 srt 2)
76
New cards
The failure of a circuit board interrupts work by a computing system until a new board is delivered. Delivery time X is uniformly distributed over the interval of at least one but no more than five days. That is X\~U\[1, 5\]. The probability that the delivery time is two or more days.
0\.75
77
New cards
A diameter X of a shaft produced has a normal distribution with parameters μ=1.005,σ=0.01. The shaft will meet specifications if its diameter is between 0.98 and 1.02 cm. Which percent of shafts will not meet specifications?
0\.073
78
New cards
Let X = monthly sick leave time have normal distribution with parameters μ= 200 hours and  σ=20 hours. What amount of time X0 should be budgeted for sick leave so that the budget will not be exceeded with 80% probability?
216\.8
79
New cards
Let X\~N(5,4).

Find P(4
0\.2026
80
New cards
Consider a Normal random variable X with E\[X\]=5 and Var(X) =16.

Find P(|X-5|>6).
0\.1336
81
New cards
The time x (in minutes) until an enzyme successfully catalyzes a biochemical reaction is approximated by this CDF:

FX(x)=1−e−x1.4,forx≥0.

What proportion of reactions is complete within 0.5 minutes?
0\.3
82
New cards
The number of calls to the call center has Poisson distribution with the rate λ = 4 calls per minute. What is the probability that we have to wait more than 20 seconds for the next call?
0\.2676
83
New cards
The total monthly rainfall (in inches) for a particular region can be modeled using Gamma distribution with α=2andβ=1.6. The mean and variance of the monthly rainfall.
E(X) =  3.2 and V(X) = 5.12
84
New cards
The total monthly rainfall (in inches) for a particular region can be modeled using Gamma distribution with α=2andβ=1.6 The probability that the total monthly rainfall exceeds 5 inches.
0\.181
85
New cards
The failures of medical devices can be modeled as a Poisson process.  Assume that units that fail are repaired immediately and the mean number of failures per hour is 0.0001.  Let X denote the time until 4 failures occur.  What is the probability that X exceed 40,000 hours \~=4.5 years?
0\.433
86
New cards
In a XYZ car company car saleswoman has to sell 1 car. She is provided with a very large (infinite for practical purposes) list of customers. She approaches customers sequentially according to the list. The probability that she makes a successful sale to any given customer is 0.2. She stops as soon as she sells the car. Suppose that all the customers behave independently of each other. Find the expected value and variance of the total number of customers the saleswoman has to approach.
E(X) = 5 and V(X) = 20
87
New cards
In a XYZ car company car saleswoman has to sell 1 car. She is provided with a very large (infinite for practical purposes) list of customers. She approaches customers sequentially according to the list. The probability that she makes a successful sale to any given customer is 0.2. She stops as soon as she sells the car. Suppose that all the customers behave independently of each other. Given that the first 5 sales were failed sales, find the probability that there will be at least 9 more failed sales before a successful sale.
(0.8)^9
88
New cards
When Paul plays pen and paper game against his favorite computer program, he wins with probability 0.60, loses with probability 0.10, and 30% of the games result is a draw. Assuming independence, find the probability that Paul’s first win happens when he plays his third game.
\~ 0.096
89
New cards
You pay $6 to play a game in which you roll a fair die. If you roll a 6, you get $8. If you roll a 5, you get $7. For any other number, you get $4. What are your expected net winnings?
\-$0.83
90
New cards
In how many ways can 5 letters be posted in 3 post boxes, if any number of letters can be posted in all of the three post boxes?
3\*3\*3\*3\*3
91
New cards
When Paul plays pen and paper game against his favorite computer program, he wins with probability 0.60, loses with probability 0.10, and 30% of the games result is a draw. Assuming independence, find the probability that Paul wins at least 8 games in 12 games.
\~ 0.438178
92
New cards
Peter’s hamburger restaurant buys some hamburger patties infected with e-coli. The probability that the e-coli survives cooking at Bob’s is 0.3. If 100 patties are cooked, what is the expected number of patties which will have no living e-coli after cooking?
70
93
New cards
 Let the random variable X be the number of heads observed in 4196 tosses of a fair coin, then E(X2) is  
4402653
94
New cards
Professor Peter makes mistakes in class according to Poisson process with an average rate of 1.2 mistakes per class. What is the probability that Peter makes exactly 10 mistakes during two weeks of classes (that is, during 6 classes, since Peter teaches a MWF lecture)?
\~0.0770
95
New cards
When Paul plays pen and paper game against his favorite computer program, he wins with probability 0.60, loses with probability 0.10, and 30% of the games result is a draw. Assuming independence, find the probability that Paul’s fifth win happens when he plays his eighth game.
\~0.17418
96
New cards
When Paul plays pen and paper game against his favorite computer program, he wins with probability 0.60, loses with probability 0.10, and 30% of the games result is a draw. Assuming independence, find the probability that Paul wins 7 games, if he plays 10 games.
\~ 0.21499
97
New cards
In a region, 15% of the adult population are smokers, 0.86% are smokers with emphysema, and 0.24% are nonsmokers with emphysema. What is the probability that a person, selected at random, has emphysema?
0\.0110
98
New cards
An ABC automobile insurance company classifies each driver as a good risk, a medium risk, or a poor risk. Of those currently insured, 30% are good risks, 50% are medium risks, and 20% are poor risks. In any given year, the probability that a driver will have a traffic accident is 0.1 for a good risk, 0.3 for a medium risk, and 0.5 for a poor risk.  The company announced that it will raise the insurance premiums for the drivers who either are poor risks or had a traffic accident during 2020, or both. What proportion of customers would have their premiums raised?
0\.38
99
New cards
The probability that 4 novels, 3 mathematics books and 2 stats books be arranged on a shelf if the mathematics books must be together and the novels must be together?
( 4!4!3!)/9!
100
New cards
A college library has five copies of a certain text on reserve. Three copies (1, 2 and 3) are first printings, and the other two (4, and 5) are second printings. A student examines these books in random order, stopping only when a second printing has been selected. One possible outcome is 5, and another is 214.The number of sample points in the sample space S is
n(S) = 32