WorksheetsEngData_Mod6_Quiz
Total questions: 50
Worksheet time: 25mins
A discrete random variable represents outcomes that are:
Always equal
Continuous and infinite
Random but non-numeric
Countable and finite
The probability mass function (PMF) gives:
The rate of change in probability
The probability of each possible discrete outcome
The slope of a variable
The area under a curve
For a valid PMF, the sum of all probabilities must be:
Infinite
1
0
Equal to number of outcomes
The cumulative distribution function (CDF) of a random variable X gives:
P(X ≤ x)
P(X = x)
P(X > x)
P(X ≠ x)
If P(X=1)=0.3, P(X=2)=0.5, and P(X=3)=0.2, then the probability that X ≤ 2 is:
0.3
0.8
0.5
1.0
A factory produces 10 light bulbs, 2 of which are defective. If two bulbs are chosen randomly, the random variable "number of defective bulbs" is:
Continuous random variable
Non-random variable
Uniform variable
Discrete random variable
A student flips a fair coin 5 times and counts the number of heads. This is an example of:
Geometric distribution
Poisson distribution
Binomial distribution
Hypergeometric distribution
In a binomial distribution, each trial must be:
Linked to previous results
Dependent and continuous
Interrelated and varying
Independent with two possible outcomes
The probability of success in each Bernoulli trial is denoted by:
n
r
p
q
If a coin is tossed 3 times, the probability of getting exactly 2 heads is:
1/2
1/4
1/8
3/8
A defective sensor has a 10% chance of failing in one test. The probability it passes all 3 tests is:
0.9 × 0.9 × 0.9 = 0.729
0.3
0.81
0.1
In a geometric distribution, the variable X represents:
The total number of trials always
The trial number of the first success
The number of failures after success
The average number of outcomes
The probability of first success on the third trial if p=0.2 is:
0.2
0.8
0.04
(0.8)^2 × (0.2) = 0.128
A geometric distribution applies when:
Trials are independent with constant success probability
Events are dependent
Probabilities vary per trial
Outcomes are continuous
A hypergeometric distribution applies when:
Events are infinite
Sampling is with replacement
Sampling is without replacement
Trials are independent
A box has 5 red and 7 blue balls. Two balls are drawn without replacement. The probability that both are red follows a:
Geometric distribution
Hypergeometric distribution
Binomial distribution
Poisson distribution
If a bus arrives on average 4 times per hour, the number of arrivals per hour follows which distribution?
Geometric distribution
Binomial distribution
Hypergeometric distribution
Poisson distribution
A Poisson distribution is often used for:
Predicting uniform outcomes
Comparing two populations
Counting rare events over time or space
Measuring continuous growth
The Poisson distribution parameter λ represents:
Average rate of occurrence
Probability of failure
Standard deviation
Number of trials
A website gets 3 customer signups per minute on average. The probability that exactly 2 signups occur in a minute follows a:
Binomial model
Poisson model
Uniform model
Geometric model
The PMF of a Poisson distribution depends on:
The probability of success p
The sampling size
The mean occurrence rate λ
The number of trials n
A discrete random variable X taking values 0,1,2 with probabilities 0.2, 0.5, 0.3 respectively has a valid PMF because:
Events overlap
Probabilities vary
All probabilities sum to 1
Probabilities are negative
For a binomial experiment with n=4 and p=0.5, the probability of getting at least one success is:
0.75
0.25
1 - (0.5)^4 = 0.9375
0.5
A hospital's emergency room gets an average of 4 new patients per hour. What is the probability that exactly 3 new patients will arrive in the next hour?
About 22.4%
About 25.0%
About 19.5%
About 15.6%
In real-world terms, the Poisson distribution could model:
The time between bus arrivals
The number of emails received per hour
The average rainfall per year
The height of individuals
What is the correct answer to question 1?
Uncountable and infinite
Not measurable
Continuous
Countable and finite
What is the correct answer to question 2?
The mean of all outcomes
The probability of each possible discrete outcome
The sum of all probabilities
The variance of outcomes
What is the correct answer to question 3?
0
1
0.5
2
What is the correct answer to question 4?
P(X ≤ x)
P(X > x)
P(X = x)
P(X < x)
What is the correct answer to question 5?
0.2
0.8
0.5
1.0
What is the correct answer to question 6?
Continuous random variable
Binomial random variable
Hypergeometric random variable
Discrete random variable
What is the correct answer to question 7?
Poisson distribution
Normal distribution
Binomial distribution
Exponential distribution
What is the correct answer to question 8?
Dependent with multiple outcomes
Independent with multiple outcomes
Dependent with two possible outcomes
Independent with two possible outcomes
What is the correct answer to question 9?
n
q
p
r
What is the correct answer to question 10?
1/8
1/4
1/2
3/8
What is the correct answer to question 11?
0.9 × 0.9 × 0.9 = 0.729
0.8 × 0.8 × 0.8 = 0.512
0.7 × 0.7 × 0.7 = 0.343
0.6 × 0.6 × 0.6 = 0.216
What is the correct answer to question 12?
The number of trials
The trial number of the first success
The probability of success
The mean number of successes
What is the correct answer to question 13?
(0.8)² × (0.1) = 0.064
(0.8) × (0.2) = 0.16
(0.8)² × (0.2) = 0.128
(0.2)² × (0.8) = 0.032
What is the correct answer to question 14?
Trials are independent with constant success probability
Trials are dependent with changing success probability
Trials are independent with changing success probability
Trials are dependent with constant success probability
What is the correct answer to question 15?
Sampling is with replacement
Sampling is without replacement
Sampling is random
Sampling is stratified
What is the correct answer to question 16?
Binomial distribution
Poisson distribution
Hypergeometric distribution
Normal distribution
What is the correct answer to question 17?
Binomial distribution
Normal distribution
Exponential distribution
Poisson distribution
What is the correct answer to question 18?
Counting frequent events over time or space
Counting rare events over time or space
Counting average events over time or space
Counting all events over time or space
What is the correct answer to question 19?
Average rate of occurrence
Total rate of occurrence
Maximum rate of occurrence
Minimum rate of occurrence
What is the correct answer to question 20?
Binomial model
Poisson model
Normal model
Exponential model
What is the correct answer to question 21?
The mean occurrence rate μ
The mean occurrence rate σ
The mean occurrence rate λ
The mean occurrence rate θ
What is the correct answer to question 22?
All probabilities sum to 0
All probabilities sum to 0.5
All probabilities sum to 1
All probabilities sum to 2
What is the correct answer to question 23?
1 - (0.5)^4 = 0.0625
1 - (0.5)^4 = 0.5
1 - (0.5)^4 = 0.9375
1 - (0.5)^4 = 0.25
What is the correct answer to question 24?
About 9.5%
About 29.5%
About 19.5%
About 39.5%
What is the correct answer to question 25?
The number of emails received per day
The number of emails received per hour
The number of emails received per week
The number of emails received per month
