
Q3 EXAM STAT REVIEWER 1
Quiz by JONALD ROSARIO
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A senior high school student is conducting a survey about transportation to school. They record the number of minutes it takes for each student to travel from home to school each day. Based on this situation, answer the question below.
Which of the following best defines a random variable?
A senior high school student is conducting a survey about transportation to school. They record the number of minutes it takes for each student to travel from home to school each day. Based on this situation, answer the question below.
What type of random variable represents the number of minutes it takes for each student to travel from home to school each day?
Which of the following is an example of a discrete random variable?
A. The distance traveled to school in kilometers.B. The amount of water consumed in a day.C. The number of absences in a school month. D.
Why is the number of minutes it takes for each student to travel from home to school each day considered a continuous random variable?
How does a discrete random variable differ from a continuous random variable?
A student records the number of classmates who submit their assignments on time each day. Which of the following correctly identifies the random variable and its type?
A teacher measures the amount of time (in hours) students spend reviewing for a quiz. If the random variable is the time spent reviewing, which of the following could be a possible set of values?
Consider a random variable representing the number of school activities attended by a student in a month. Which option correctly identifies the variable and its possible values?
A student tracks the number of quizzes given each day for one week and records the following data: {1, 0, 2, 1, 3, 0, 2}. Which of the following represents the possible values of the random variable “number of quizzes given in a day”?
A student recorded the number of homework assignments submitted by classmates in a week. The recorded values were {1, 2, 0, 3, 2, 1, 0, 2, 4, 3}. Another student claims that the possible values of the random variable “number of homework submissions” are {0, 1, 2, 3, 4}.
How would you evaluate this claim?
What is the sum of all probabilities in the probability distribution of a discrete random variable?
For a spinner divided into 8 equal sections, what is the probability of landing on any specific section?
Why is the outcome of spinning a spinner with 8 equal sections considered a discrete random variable?
Which statement best describes the probability distribution of spinning a fair spinner with 8 equal sections?
A game involves spinning a fair spinner with 8 equal sections numbered 1 to 8. If the random variable X represents the outcome, what is the probability that X is an even number?
A quality control officer records the number of customer complaints received in a day. The random variable X represents the number of complaints, and its probability distribution is shown below. Use the information to answer the question that follows.
x (Number of Complaints) 0 1 2 3
P(x) 0.25 0.35 0.25 0.15
Which formula is used to compute the mean (μ) of the discrete random variable X?
In a probability distribution, what is the sum of all probabilities?
A quality control officer records the number of customer complaints received in a day. The random variable X represents the number of complaints, and its probability distribution is shown below. Use the information to answer the question that follows.
x (Number of Complaints) 0 1 2 3
P(x) 0.25 0.35 0.25 0.15
Why is the given table considered a valid probability distribution?
A quality control officer records the number of customer complaints received in a day. The random variable X represents the number of complaints, and its probability distribution is shown below. Use the information to answer the question that follows.
x (Number of Complaints) 0 1 2 3
P(x) 0.25 0.35 0.25 0.15
What is the mean (μ) of the given probability distribution? (Round off your answer up to 2 decimal places.)
A quality control officer records the number of customer complaints received in a day. The random variable X represents the number of complaints, and its probability distribution is shown below. Use the information to answer the question that follows.
x (Number of Complaints) 0 1 2 3
P(x) 0.25 0.35 0.25 0.15
Compute the variance (σ2) of the given probability distribution. (Round off your answer up to 2 decimal places.)
The following probability distribution represents the number of defective items produced by a machine during a shift:
x (Number of Defective Items) 0 1 2 3
𝑃(x) 0.2 0.5 0.2 0.1
Given that the mean of X is 1.1, what impact would increasing the probability of X=0 to 0.4 have on the variance?
Consider the following probability distribution for a random variable X:
x (Number of Defective Items) 0 1 2 3
𝑃(x) 0.3 0.4 0.2 0.1
If the mean of X is 1.1, how would a decrease in the probability of X=1 affect the variance?
The number of customer complaints received daily by a service center is modeled by the probability distribution below:
x 0 1 2 3
P(x) 0.45 0.25 0.20 0.10
If the mean is 1.0 and the variance is 1.10, which conclusion is correct?
Given the following probability distribution for a discrete random variable X, where X represents the number of defective items:
X (Number of Defective Items) 0 1 2 3
𝑃(x) 0.49 0.49 0.01 0.01
The mean of X is1.0, and the variance is 0.02. Which of the following best describes this distribution?
A restaurant manager records the number of customer complaints received per day. Based on 30 days of observation, the probability distribution of complaints per day is shown below. The manager claims that the restaurant rarely receives complaints, with only 1 complaint per day on average.
Number of Students (X) 0 1 2 3 4
Probability P(X) 0.33 0.13 0.23 0.15 0.16
Determine the mean of the probability distribution and evaluate if the manager’s claim is valid.