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Questions in this quiz (73)
1Two events each have probability 0.3 of occurring and are independent. The probability that neither occur is
- A0.49
- B0.51
- C0.3
- D0.6
- Enone of the given answers
2A class consists of 490 female and 510 male students. The students are divided according to their marks Passed and Did not pass
Passed Did not pass
Female 430 60
Male 410 100
If one person is selected randomly, what is the probability that it did not pass given that it is male.- A0.17
- B0.21
- C0.42
- D0.08
- E0.196
3A student can solve 6 from a list of 10 problems. For an exam 8 questions are selected at random from the list. What is the probability that the student will solve exactly five problems?
- A0.98
- B0.02
- C0.28
- D0.53
- Enone of the shown answers
4Suppose that 10% of people are left-handed. If 6 people are selected at random, what is the probability that exactly 2 of them are left-handed?
- A0.0100
- B0.031
- C0.098
- D0.29
- E0.053
5105. Suppose a computer chip manufacturer rejects 15% of the chips produced because they fail presale testing. If you test 4 chips, what is the probability that not all of the chips fail?
- A0.9995
- B0.00005
- C0.15
- D0.6
- E0.5220
6Which of these has a Geometric model?
- Athe number of aces in a five-card Poker hand
- Bthe number of people we survey
- Cthe number of people in a class of 25 who have taken Statistics
- Dthe number of people we survey until we find someone who has taken Statistics
- Ethe number of sodas students drink per day
7T 0 1 2
P(T=t) 0.4 0.4 0.2
Find .
The answer is 0.4- A0.8
- B0.4
- C0.3
- D0.2
- E0
8Which of the following is an example of a discrete random variable?
- AThe distance you can drive in a car with a full tank of gas.
- BThe weight of a package at the post office.
- CThe amount of rain that falls over a 24-hour period.
- DThe number of cows on a cattle ranch.
- EThe time that a train arrives at a specified stop.
9Which of the following is the appropriate definition for the union of two events A and B?
- AThe set of all possible outcomes.
- BThe set of all basic outcomes contained within both A and B.
- CThe set of all basic outcomes in either A or B, or both.
- DNone of the given answers
- EThe set of all basic outcomes that are not in A and B.
10Johnson taught a music class for 20 students under the age of ten. He randomly chose one of them. What was the probability that the student was under eleven?
- A1
- B0.5
- C1/25
- D0
- E0.25
11A regular deck of 52 cards contains 4 different suits (Spades, Hearts, Diamonds, and Clubs) that each have 13 cards. If you randomly choose two cards from the deck, what is the probability that both cards will all be Spades?
- A1/17
- B2/17
- C1/4
- D4/17
- E33/68
12112. A standard deck of 52 cards contains 4 different suits (Spades, Hearts, Diamonds, and Clubs) that each have 13 cards. What is the probability of drawing a Diamond from a standard deck of 52 cards?
- A1/52
- B13/39
- C1/13
- D1/4
- E1/2
13One card is randomly selected from a shuffled deck of 52 cards and then a die is rolled. Find the probability of obtaining an Ace and rolling an odd number.
- A1/104
- B7/13
- C1/39
- D1/26
- E1/36
14The number of clients arriving each hour at a given branch of a bank asking for a given service follows a Poisson distribution with parameter λ=4. It is assumed that arrivals at different hours are independent from each other. The probability that in a given hour at most 2 clients arrive at this specific branch of the bank is:
- A2e^(-4)
- B3e^(-4)
- C6e^(-4)
- D8e^(-4)
- E8e^(-2)
15116. Table shows the cumulative distribution function of a random variable X. Determine .
X 1 2 3 4
F(X) 1/8 1/4 3/4 1
ANSWER IS 3/4- A1/8
- B5/8
- C1/2
- D3/4
- E1/3
16If P(A)=1/2 and P(B)=1/2 then P(A∩B)=
- A1/4, always
- B1/4, if A and B are independent
- C1/2, always
- D1/2, if A and B are independent
- Enone of the given answers
17Suppose that P(A|B)=3/5, P(B)=2/7, and P(A)=1/4. Determine P(B|A).
- A24/75
- B24/35
- C6/35
- D12/75
- ENone
18The mathematical expectation and dispersion of a random variable X distributed under the binomial law are …, respectively.
- AEX=np,DX=npq
- BEX=npq,DX=np
- CEX=C_n^k np,DX=npq
- DEX=np,DX=C_n^k npq
- EEX=np,DX=λ
19The probability distribution function of random variable X~Geom(p) is
- AP(X=m)=pq^(m-1)
- Bнажми и запомни его
20The mathematical expectation and dispersion of a random variable X having the geometrical distribution with the parameter p are …, respectively.
- AEX=1/p,DX=q/p^2
- BEX=npq,DX=np
- CEX=1/p,DX=p/q^2
- DEX=q/p,DX=q/p^2
- EEX=np,DX=λ
21122. The Lakers scored the following numbers of goals in their last twenty matches:
3, 0, 1, 5, 4, 3, 2, 6, 4, 2, 3, 3, 0, 7, 1, 1, 2, 3, 4, 3
Which number had the highest frequency?- A3
- B6
- C7
- D2
- E4
22123. 60 students sat a test. The frequency distribution is shown in the following table: How many students scored 5 or more?
- A11
- B33
- C38
- D22
- E25
23A fair die was thrown 100 times. The frequency distribution is shown in the following table: how many throws scored greater than 2, but less than or equal to 5?
- A26
- B45
- C44
- D63
- E52
24The children in a class did a survey of the number of siblings (brothers and sisters) each of them had. The results are recorded in the following table:
How many families had more than 4 children?
- A4
- B8
- C5
- D13
- E9
25Rachel rolled a die forty five times with the following results: what was her mean score?
- A3.5
- B3.4
- C3.62
- D7.5
- E6.3
26Ramiro did a survey of the number of pets owned by his classmates, with the following results: what was the mean number of pets?
- A2.13
- B1.8
- C2.57
- D30
- E2
27A machine produces electrical components. 99.7% of the components have lengths between 1.176 cm and 1.224 cm. Assuming this data is normally distributed, what are the mean and standard deviation?
- AE(X)=1.210, std = 0.008
- BE(X) = 1.200, std = 0.008
- CE(X) = 1.120, std = 0.008
- DE(X) = 1.200, std = 0.004
- EE(X) = 1.1250, std = 0.004
28A booklet has 12 pages with the following numbers of words:
271, 354, 296, 301, 333, 326, 285, 298, 327, 316, 287 and 314
What is the median number of words per page?- A301
- B307.5
- C305.5
- D314
- Ecannot determine
29If a researcher wants to study a binomial population where p = 0.1, what is the minimum size n needed to make use of the central limit theorem?
- A0
- B100
- C10
- D10000
- E1000
30As a general rule, approximately what is the smallest sample size that can be safely drawn from a non-normal distribution of observations if someone wants to produce a normal sampling distribution of sample means?
- An = 20
- Bn = 30
- Cn = 40
- Dn = 50
- En = 60
31There are ten sprinters in the finals of a race. How many different ways can the gold, silver and bronze medals be awarded?
- A120
- B710
- C1440
- D100
- E60
32133. A survey of a group’s viewing habits over the last year revealed the following information:
(i) 28% watched gymnastics
(ii) 29% watched baseball
(iii) 19% watched soccer
(iv) 14% watched gymnastics and baseball
(v) 12% watched baseball and soccer
(vi) 10% watched gymnastics and soccer
(vii) 8% watched all three sports.
Calculate the percentage of the group that watched none of the three sports during the last year.- A52%
- B24%
- C41%
- D36%
- E20%
33You are given P[A∪B]=0.7 and P[A∪B^' ]=0.9. Determine P[A]
- A0.2
- B0.6
- C0.4
- D0.3
- E0.8
34An electronic system contains three cooling components that operate independently. The probability of each component’s failure is 0.05. The system will overheat if and only if at least two components fail. Calculate the probability that the system will overheat.
- A0.045
- B0.098
- C0.007
- D0.135
- E0.143
35The number of days an employee is sick each month is modeled by a Poisson distribution with mean 1. The numbers of sick days in different months are mutually independent. Calculate the probability that an employee is sick more than two days in a three-month period.
- A0.199
- B0.224
- C0.577
- D0.423
- E0.801
36What is the covariance between X and Y?
X
4.0 7.0
Y 3.0 30% 15%
5.0 25% 30%- A-0.9727
- B0.3150
- C1.4842
- D4.9224
- E3.5236
37What is the arithmetic mean for XYZ stock?
2003 2004 2005 2006 2007 2008
22% 5% -7% 11% 2% 11%- A7.3%
- B8%
- C9%
- D11%
- E7%
38What is the median return for XYZ stock?
2003 2004 2005 2006 2007 2008
22% 5% -7% 11% 2% 11%- A7.3%
- B8%
- C11%
- D10%
- E2%
39What is the mode of the returns for XYZ stock?
2003 2004 2005 2006 2007 2008
22% 5% -7% 11% 2% 11%- A22%
- B11%
- C5%
- D2%
- E10%
40At a charity ball, 800 names are put into a hat. Four of the names are identical. On a random draw, what is the probability that one of these four names will be drawn?
- A0.004
- B0.005
- C0.001
- D0.01
- E0.03
41Two events are said to be independent if the occurrence of one event:
- AMeans that the second event cannot occur
- BDoes not affect the probability of the occurrence of the other event
- CMeans that the second event is certain to occur
- DNo right answer
- EMeans that the first event is certain to occur
42The mathematical expectation and dispersion of a random variable X having the uniformly distribution on [a,b] are …, respectively.
- AEX=(a+b)/2, var(X)=(b-a)^2/12
- BEX=(a-b)/2, DX=(b-a)^2/12
- CEX=(a+b)/2, DX=(b+a)^2/12
- DEX=q/p, DX=q/p^2
- EEX=(a+b)/2,DX=(b-a)^2/15
43For a continuous random variable X, the probability of any single value of X is:
- A1
- B0
- Cdetermined by the CDF
- Ddepends on the function
- ENone of the given answers
44A study of automobile accidents produced the following data:
an automobile from one of the model years 1997, 1998, and 1999 was involved in an accident. Determine the probability that the model year of this automobile is 1997.
- A0.22
- B0.45
- C0.30
- D0.33
- E0.50
45What is moment generating function?
- AM_X (t)=E(e^(-tx) )
- BM_X (t)=E(e^tx )
- CM_X (t)=E(e^2tx )
- DM_X (t)=E(e^t )
- EM_X (t)=E(e^x )
46Given following moment generating function
To which type of distribution this MGF is used?
- APoisson
- Bnormal
- Cgeometric
- Dpareto
- Euniform
47The Poisson distribution can be viewed as providing an approximation to the Binomial distribution when
- AThe sample size is large, and probability of ‘success’ is very small
- BThe sample size is small, and probability of ‘success’ is very small
- CThe sample size is small, and probability of ‘success’ is very large
- DThe sample size is large, and probability of ‘success’ is very large
- ENo approximations exists
48MGF of the Poisson distribution
- A
- B
- Clambda
- Ddoes not exist
- E
- A
49First derivative of MGF at t=0 is
- Avariance
- Bexpected value
- C0
- Dfunction, depending on t
- Eno such thing exists
50Given following joint probability distribution table. Find E(X)-?
- A1/3
- B1/2
- C1
- D0
- E1/4
51Given following joint probability distribution table. Find E(Y)-?
- A-1/3
- B-1/2
- C1/8
- D0
- E-1/4
52Given following joint probability distribution table. Find cov(X,Y)-?
- A1/3
- B-1/4
- C1/2
- D0
- E1/4
53Given following joint probability distribution table. Find E(Y|X=1)-?
- A-1/3
- B-2/3
- C1/2
- D2/3
- E1/3
54Given following joint probability distribution table. Find whether X and Y are independent
- ADependent, as their product of marginal densities equal joint density for every possible pair (x,y)
- BDependent, the product of the marginal densities does not equal the joint density for every possible pair (x,y)
- CIndependent, as their product of marginal densities, equal joint density for every possible pair (x,y)
- DCan't determine
- E0
55Let X and Y be discrete random variables with joint probability function given by the following table:
Find E(X)?
- A1
- B2.85
- C0.05
- D3.5
- E2.50
56Let X and Y be discrete random variables with joint probability function given by the following table:
Find E(Y)?- A2.85
- B1
- C0.05
- D3.5
- E2.50
57Let X and Y be continuous random variables with joint density function
Determine the conditional density function of Y given X=x, where 0<x<1
- A2(1-x), x<y<1
- B1/(1-x), x<y<1
- C2, x<y<1
- D1/y, x<y<1
- E1/(1-y), x<y<1
58We are given the probability distribution functions of two random variables X and Y shown in the tables below.
X 1 3 Y 2 4
P 0.4 0.6 P 0.2 0.8
Find E[X+Y].- A5.8
- B2.2
- C2
- D8.8
- E10
59An urn contains 10 balls: 4 red and 6 blue. A second urn contains 16 red balls and an unknown number of blue balls. A single ball is drawn from each urn. The probability that both balls are the same color is 0.44. Calculate the number of blue balls in the second urn.
- A44
- B4
- C16
- D20
- E24
60An insurance company examines its pool of auto insurance customers and gathers the following information:
i) All customers insure at least one car
ii) 70% of the customers insure more than one car
iii) 20% of the customers insure a sports car
iv) Of those customers who insure more than one car, 15% insure a sports car.
What is the probability that a randomly selected customer insures exactly one car, and that car is not a sports car?- A0.205
- B0.200
- C0.131
- D0.250
- E0.300
61An insurance company examines its pool of auto insurance customers and gathers the following information:
v) All customers insure at least one car
vi) 64% of the customers insure more than one car
vii) 20% of the customers insure a sports car
viii) Of those customers who insure more than one car, 15% insure a sports car.
What is the probability that a randomly selected customer insures exactly one car, and that car is not a sports car?- A0.200
- B0.256
- C0.131
- D0.205
- E0.300
62An auto insurance company insures drivers of all ages. An analyst compiled the following statistics on the company’s insured drivers:
- A0.13
- B0.16
- C0.19
- D0.23
- E0.4
63Given a normal distribution with µ=90 and σ=10, what is the probability that X>75?
- A0.93
- B0.25
- C0.49
- D0.45
- E0.01
64Let X, and Y be the lifespans (in hours) of two electronic devices, and their joint probability density function is given below:
Determine the value of c
- A6
- B3/2
- C12
- D1
- E2
65Let X, and Y be the lifespans (in hours) of two electronic devices, and their joint probability density function is given below:
Determine the value c
- A2
- B3/2
- C12
- D1
- E4
66A bag contains blue and red balls. Two balls are drawn randomly without replacement. The probability of selecting a blue and then a red ball is 0.2. The probability of selecting a blue ball in the first draw is 0.5. What is the probability of drawing a red ball, given that the first ball drawn was blue?
- A0.4
- B0.2
- C0.1
- D0.5
- E0.3
67A die is rolled thrice. What is the probability that the sum of the rolls is at least 5.
- A212/216
- B216/216
- C1/6
- D3/216
- E6/216
68In a class, 40% of the students study math and science. 60% of the students study math. What is the probability of a student studying science given he/she is already studying math?
- A0.67
- B0.40
- C0.60
- D0.33
- E0.50
69Suppose that the probability of event A is 0.2 and the probability of event B is 0.4. also, suppose that the two events are independent. Then P(A|B) is:
- AP(A) = 0.2
- BP(A)/P(B) = ½
- CP(A)P(B) = 0.08
- DNone of the above
- EP(B) = 0.4
70Find the probability of selecting a black card or a 6 from a deck of 52 playing cards
- A7/13
- B26/52
- C4/52
- D13/52
- E36/52
71What is the probability of drawing a king and a queen consecutively from a deck of 52 cards, without replacement.
- A4/663
- B1/13
- C4/51
- D12/2652
- E1/2652
72The fair dice is rolled. What is the probability of getting 5?
- A1/6
- B2/6
- C3/6
- D1
- E6
73The fair coin was flipped twice. What is the probability of obtaining two heads?
- A1/4
- B1/5
- C1/2
- D1/3
- E1
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- Quiz on Untitled, created by Tamerlan Sandykbaev on 26/12/2019.
- Author
- Tamerlan Sandykbaev
- Language
- English
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