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STATISTICS AND PROBABILITY SUMMATIVE Flashcards | StudBud
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STATISTICS AND PROBABILITY SUMMATIVE
STATISTICS AND PROBABILITY SUMMATIVE
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1
What is the probability that a standard normal variable Z is less than 1.5?
C) 0.6915
D) 0.5987
A) 0.9332
B) 0.8413
2
Which of the following statements is true about the sample space in an experiment?
It is the set of all observed outcomes in an experiment
It is the set of all predicted outcomes in an experiment
It is the set of all impossible outcomes in an experiment
It is the set of all possible outcomes in an experiment
3
What is the mean of a standard normal distribution?
D) 2
A) 0
B) 1
C) -1
4
Find the standard deviation if the variance is 4.
B. -1
C. 2
D. -2
A. 1
5
5 people are ran. selected, find the probability that exactly 3 of them prefer the new product if 60% prefer new product
D) (5C3)⋅(0.6)^2⋅(0.4)^2
C) (5C3)⋅(0.6)^3⋅(0.4)^3
B) (5C3)⋅(0.6)^2⋅(0.4)^3
A) (5C3)⋅(0.6)^3⋅(0.4)^2
6
If the mean of a discrete random variable Y is 4 and the variance is 2, which of the following statements is true?
C) The standard deviation of Y is √2
A) The standard deviation of Y is 2
B) The standard deviation of Y is 4
D) The standard deviation of Y is √4
7
Time taken to produce each item (X) and the number of defective items produced by a machine in a day (y).
X is discrete, Y is discrete
X is discrete, Y is continuous
X is continuous, Y is continuous
X is continuous, Y is discrete
8
Find the corresponding value of the normal random variable X with a mean of 30 and a standard deviation of 5 if z=-1.2?
D) X=27
C) X=26
B) X=25
A) X=24
9
What is the probability of drawing an Queen from a standard deck of 52 playing cards?
A) 1/13
B) 1/26
C) 1/52
D) 4/52
10
In a standard normal distribution, what is the z-score that corresponds to the area=0.3238?
B) 0.93
C) 0.94
A) 0.92
D) 0.95
11
Find the 95th percentile of the standard normal distribution.
A) 1.28
D) 2.33
B) 1.64
C) 1.96
12
Which is true about the probability of each value of a random variable in a discrete probability distribution?
B) It must be less than 0
A) It must be greater than 1
C) It must be between or equal to 0 and 1
D) It can be any real number
13
Which of the following lists all possible values of X when flipping a coin four times?
D) 0, 1, 2
A) 0, 1, 2, 3
C) 1, 2, 3
B) 0, 1, 2, 3, 4
14
Given X with possible values 1,2,3 and corresponding probabilities 0.2,0.5,0.3, what is the variance of X?
D) 0.86
C) 0.76
A) 0.56
B) 0.66
15
Which of the following is a characteristic of a discrete probability distribution?
C) The sum of the probabilities of all values is equal to 1
D) The probabilities of the values can be greater than 1
A) The probabilities of the values can be negative
B) The sum of the probabilities of all values is less than 1
16
Which of the following is an example of a continuous random variable?
The number of students in a classroom
The height of students in a class
The number of cars in a parking lot
The number of defective items produced by a machine
17
Z has possible values 0,1,2 with corresponding probabilities 0.3,0.4,0.3. What is the mean of Z?
D) 1.2
C) 1.1
A) 0.9
B) 1.0
18
Which of the following best describes the variance of a discrete random variable?
A) The average value of all possible outcomes
B) The measure of how spread out the values of the random variable are
D) The most frequently occurring value of a random variable
C) The highest value a random variable can take
19
Given P(Y=1)=0.4, P(Y=2)=0.3, and P(Y=3)=0.2, does this distribution satisfy the properties of a prob. distribution?
C) Yes, because each probability is between 0 and 1
D) No, because one of the probabilities is greater than 1
A) Yes, because the sum of the probabilities is 1
B) No, because the sum of the probabilities is not 1
20
Given the following probability distribution: P(X=1)=0.4, P(X=2)=0.3, P(X=3)=0.5, what is the sum?
A) 0.8
D) 0.5
C) 1.2
B) 1.0
21
Which of the following is a continuous random variable representing the height of students in a classroom?
160.5 cm
170.75 cm
All of the above
150 cm
22
If the area to the right of Z is 0.025, what is the value of Z?
C) 2.33
B) 1.64
A) 1.96
D) 2.58
23
Calculate the probability of getting exactly two tails when flipping a coin three times. .
D) ¾
B) 3/8
A) 1/8
C) 1/2
24
What does the mean (expected value) of a discrete random variable represent?
C) The most frequently occurring value of the random variable
D) difference between the highest and lowest values of the random variable
A) The highest value the random variable can take
B) average value of all possible outcomes, weighted by their probabilities
25
What percentage of the data falls within two standard deviations of the mean in a standard normal distribution?
D) 99%
C) 95%
A) 50%
B) 68%
26
Which of the following best describes the mean (expected value) of a random variable?
D) difference between the highest and lowest values of a random variable
C) The most frequently occurring value of a random variable
B) average value of all possible outcomes, weighted by their probabilities
A) The highest value a random variable can take
27
Find the variance if the standard deviation is 2.83.
C) 4
B) 6
D) 2
A) 8
28
What is the sum of the probabilities of all values of a random variable in a discrete probability distribution?
D) It can be any value
A) 0
C) 1
B) 0.5
29
For a normal random variable Y with a mean of 20 and a standard deviation of 5, what is the z-score for Y=25?
D) 2
C) 0
A) 1
B) -1
30
What does the standard deviation of a discrete random variable indicate?
D) The most frequently occurring value of the random variable
C) The highest value the random variable can take
A) The average value of all possible outcomes
B) Degree to which the values of the random variable differ from the mean
31
If the mean of a discrete random variable X is 5 and the variance is 2, which of the following statements is true?
D) The values of X are all equal to 2
C) The values of X are all equal to 5
B) The values of X are spread out around 5
A) The values of X are tightly clustered around 5
32
Which of the following statements is true about the tails of a normal distribution?
B) They are bounded and do not extend beyond a certain point
A) They extend infinitely in both directions
D) They are always negative
C) They are always positive
33
Which of the following is NOT a characteristic of a continuous random variable?
It can be measured
It can take on an infinite number of values
It can take on any value within a given range
It can take on a finite number of values
34
In a normal distribution, what percentage of the data falls within one standard deviation of the mean?
B) 68%
A) 50%
C) 95%
D) 99%
35
Find the mean of the following data set: 2, 4, 6, 8, 10.
C) 6
A) 4
D) 7
B) 5
36
X has a mean of 50 and a standard deviation of 10. What is the standard normal variable Z corresponding to X=70?
C) Z=2.5
B) Z=2.0
D) Z=3.0
A) Z=1.5
37
Prob. that a bulb is defective is p=0.05. If 12 bulbs are selected, what is the probability that exactly 5 are def.?
D) (12C5)⋅(0.05)^7⋅(0.95)^7
A) (12C5)⋅(0.05)^5⋅(0.95)^7
C) (12C5)⋅(0.05)^5⋅(0.95)^5
B) (12C5)⋅(0.05)^7⋅(0.95)^5
38
What is the total area under the standard normal curve?
D) 2.0
A) 0.5
B) 1.0
C) 1.5
39
Which of the following statements is true about discrete random variables?
They are always positive.
They are always whole numbers.
They can take on any value within a given range.
They can take on only integer value.
40
Which of the following area correspond to z=1.43?
A) 0.4222
D) 0.4265
C) 0.4251
B) 0.4236
41
If a fair six-sided die is rolled, what is the probability of rolling a 5?
A) 1/2
C) 1/4
D) 1/6
B) 1/3
42
Which property of a probability distribution satisfy the ff: P(Z=1)=0.3, P(Z=2)=0.1, P(Z=3)=0.1, and P(Z=4)=0.5.?
C) Both A and B
B) The sum of the probabilities of all values is equal to 1
D) Neither A nor B
A) The probability of each value is between 0 and 1
43
X has a mean of 100 and a standard deviation of 20, what is the value of X when the standard normal variable Z=1.75?
D) X=145
B) X=135
C) X=140
A) X=130
44
Which of the following represents the area under the standard normal curve to the left of Z=0?
B) 0.50
D) 1.00
A) 0.25
C) 0.75
45
Which of the following statements is true about the possible values of a random variable?
They are always positive
They are always negative
They are real numbers
They are always whole numbers
46
What is the mean of X with possible values 1,2,3 and corresponding probabilities 0.2,0.5,0.3?
A) 1.8
C) 2.5
B) 2.1
D) 3.0
47
If a random variable X has a mean of 10 and a standard deviation of 2, what is the probability that X is less than 8?
B) 0.8413
A) 0.1587
C) 0.5000
D) 0.0228
48
Which of the following best describes a normal distribution?
C) A distribution with a flat top
A) A distribution with two peaks
B) A distribution that is symmetric and bell-shaped
D) A distribution with a skewed shape
49
What is the shape of the standard normal distribution?
A) Uniform
B) Skewed
C) Bimodal
D) Bell-shaped
50
If a coin is flipped twice, what is the probability of getting exactly one tail?
D) 2/4
C) 1/3
A) 1/4
B) 1/2
