Q: A data professional is working for a large corporation. The marketing
team asks them to predict the success of a new ad campaign. To make an informed
prediction, they use statistics to analyze data on past ad campaigns. What type
of probability are they using?
- Dependent
- Independent
- Objective
- Subjective
Explanation: The examination of data and statistical evidence makes up the foundation of objective probability. In this particular instance, the data expert uses statistics to conduct an analysis of data from previous advertising campaigns to draw an educated conclusion on the performance of the current advertising campaign. The technique in question is characterized by the use of actual data and mathematical computations, both of which are characteristics of objective probability.
Q: The probability of an event is close to 1. Which of the following
statements best describes the likelihood that the event will occur?
- The event is unlikely to occur.
- The event is certain to occur.
- The event is certain not to occur.
- The event is likely to occur.
Explanation: Because of this, if the probability of an event is somewhat near to one, it indicates that while it is extremely probable that the event will take place, it is not certain that it will take place. The phrase "The event is likely to occur" is thus the most accurate representation of the situation.
Q: The probability of rain tomorrow is 40%. What is the probability of
the complement of this event?
- The probability of no rain tomorrow is 80%.
- The probability of no rain tomorrow is 20%.
- The probability of no rain tomorrow is 60%.
- The probability of no rain tomorrow is 40%.
Explanation: By subtracting the probability of the event from 1, one may get the probability of the occurrence that is the complement of the previously mentioned event.
Q: Fill in the blank: Two events are _____ if the occurrence of one
event does not change the probability of the other event.
- continuous
- independent
- discrete
- dependent
Explanation: The occurrence of the other event does not have any impact on the chance that the first event will subsequently take place. For instance, the act of flipping a coin and the act of rolling a die are both considered to be independent occurrences because the outcome of the coin flip does not influence the outcome of the die roll.
Q: Fill in the blank: To calculate posterior probability, a data
professional can use _____ to update the prior probability based on the data.
- the normal distribution
- Bayes’s theorem
- the binomial distribution
- the complement rule
Explanation: The use of a mathematical formula for the purpose of modifying the likelihood of hypotheses in light of fresh information or data. Furthermore, it enables the computation of posterior probabilities by combining prior probabilities with the probability of the observed data. This is an essential component of Bayesian statistics.
Q: Which of the following statements accurately describes a key
difference between discrete and continuous random variables?
- Discrete random variables are typically decimal values that can be
measured; continuous random variables are typically whole numbers that can be
counted.
- Discrete random variables are typically whole numbers that can be
counted; continuous random variables are typically decimal values that can be
measured.
- Discrete random variables are positive numbers; continuous random
variables are negative numbers.
- Discrete random variables are negative numbers; continuous random
variables are positive numbers.*
Explanation: It is possible to enumerate the number of different values that they may take on. You can count them since they are often entire numbers. For instance, the number of pupils in a classroom or the number of automobiles in a parking lot are both examples of statistics.
Q: The Poisson distribution can model which of the following kinds of
data? Select all that apply.
- The number of heads in 10 fair coin tosses
- The number of calls per hour at a call center
- The number of visitors per day on a website
- The number of customers per week at a retail store
Explanation: It is possible to model the number of times an event happens during a predetermined period of time or space by using the Poisson distribution. This is the case provided that the events occur at a known constant mean rate and regardless of the amount of time that has passed since the most recent occurrence.
Q: A data professional working for a smartphone manufacturer is
analyzing sample data on the weight of a specific smartphone. The data follows
a normal distribution, with a mean weight of 150g and a standard deviation of
10g. According to the empirical rule, approximately what percentage of the data
values lie between 140g and 160g?
Explanation: A little less than 68 percent of the values in the data are located within one standard deviation of the mean.
Q: A data value has a z-score of 2.5. Where is it located?
- 2.5 standard deviations below the median
- 2.5 standard deviations above the median
- 2.5 standard deviations below the mean
- 2.5 standard deviations above the mean
Explanation: A positive z-score implies that the value of the data is greater than the number that represents the mean of the distribution.In the event that the z-score is negative, it would provide evidence that the data value is lower than the mean of the distribution.
Q: A data analytics team at a water utility works with a dataset that
contains information about local reservoirs. They determine that the data
follows a normal distribution. What Python function can they use to compute
z-scores for the data?
- mean.zscore()
- describe()
- median.zscore()
- stats.zscore()
Explanation: It is the scipy.stats package in Python that is responsible for providing this method. It does this by calculating the z-score for each value in the dataset in relation to the mean and standard deviation of the dataset.
Q: Fill in the blank: The _____ distribution best models the number of
heads in 10 fair coin flips.
- Bernoulli
- Poisson
- Binomial
- Normal
Explanation: This circumstance is best approximated by the Binomial distribution because flipping a fair coin is a Bernoulli trial, which means that there are two potential outcomes with equal probability. Since we are interested in the number of heads that occur in ten such trials (coin flips), the Binomial distribution is the most appropriate choice.
Q: If all outcomes of an event are equally likely, how is its
probability calculated?
- Divide the number of desired outcomes by the total number of possible
outcomes.
- Divide the total number of possible outcomes by the number of desired
outcomes.
- Divide the total number of certain outcomes by the number of possible
outcomes.
- Divide the total number of possible outcomes by the number of certain
outcomes.
Explanation: Consequently, the most appropriate option is to divide the total number of possibilities that are conceivable by the number of outcomes that are wanted.
Q: A coin is tossed twice. To calculate the probability of getting two
heads in a row, which of the following equations should be used?
Explanation: In light of the fact that the results of each toss are separate events, the chance of both events happening simultaneously (receiving heads on both throws) is equal to the product of the probabilities of each of the individual outcomes.
Q: Which of the following events are mutually exclusive? Select all
that apply.
- Getting heads on a first coin toss and tails on a second coin toss
- Getting a 4 on a first die roll and a 6 on a second die roll
- Getting heads and tails on the same coin toss
- Getting a 4 and a 6 on the same die roll
Explanation: The flip of a coin cannot produce both heads and tails at the same time, thus this is not something that can happen on its own. On account of this, these occurrences cannot occur simultaneously.It is not feasible to achieve this goal since a single roll of the dice can only produce one outcome (a number that falls between 1 and 6). On account of this, these occurrences cannot occur simultaneously.
Q: What concept refers to the probability of an event before new data
is collected?
- Prior probability
- Subjective probability
- Conditional probability
- Posterior probability
Explanation: Before considering any new information or evidence, this is the chance that an event will occur based on preexisting knowledge or information.
Q: Which of the following are examples of continuous random variables?
Select all that apply.
- The number of students in a math class
- The height of a redwood tree
- The time it takes for a person to run a race
- The weight of a polar bear
Explanation: As a result of the fact that height can be measured as a real number within a range, this random variable is considered to be continuous. Because the passage of time can be quantified as a real number within a certain range, this is an example of a continuous random variable.Because weight can be measured as a real number within a range, this thing is considered to be a continuous random variable.
Q: A data professional working for a smartphone manufacturer is
analyzing sample data on the weight of a specific smartphone. The data follows
a normal distribution, with a mean weight of 150g and a standard deviation of
10g. What data value lies 3 standard deviations below the mean?
Explanation: If you have a normal distribution with a mean of 150 grams and a standard deviation of 10 grams, you need to determine the data value that is three standard deviations below the mean.
Q: The mean and the standard deviation of a standard normal
distribution always equal what values?
- Mean = 2; standard deviation = 1
- Mean = 0; standard deviation = 2
- Mean = 1; standard deviation = 2
- Mean = 0; standard deviation = 1
Explanation: By translating the data into a standard form in which the mean is equal to zero and the standard deviation is equal to one, this standardization makes it possible to understand and compare the data in a manner that is consistent across a variety of normal distributions simultaneously.
Q: A data professional is analyzing sales data for a retail store. The
data follows a normal distribution. What Python function can they use to
compute z-scores for the data?
- stats.zscore()
- median.zscore()
- mean.zscore()
- normal.zscore()
Explanation: It is the scipy.stats package in Python that is responsible for providing this method. It does this by calculating the z-score for each value in the dataset in relation to the mean and standard deviation of the dataset.
Q: A first coin toss results in tails, and a second coin toss results
in heads. What concept best describes these two events?
- Subjective
- Non-random
- Independent
- Dependent
Explanation: In the case when the occurrence of one event does not influence the likelihood of the other event, then the two occurrences are said to be independent. In this particular scenario, the result of the first coin toss, which was a tails, does not have any bearing on the result of the second coin toss, which was a heads. Each flip of the coin is a separate event that has its own probability associated with it.
Q: What concept refers to the probability of an event occurring given
that another event has already occurred?
- Classical probability
- Conditional probability
- Subjective probability
- Empirical probability
Explanation: Given the fact that another event, indicated as event B, has already taken place, this is the probability that an event, denoted as P(A∣B), will take place. The calculation for this is as follows: 𝑃 (𝐴 ∣ 𝐵) = 𝑃 (𝐴 ∩ 𝐵) 𝑃 (𝐵) ∩ 𝐵 ∩ 𝐵 ∩ 𝐵 ∩ 𝐵 ∩ 𝐵 ∩ 𝐵 ∣ 𝐵 ∣ 𝐵 ∩ 𝐵 ∣ 𝐵 ∣ 𝐵 ∣ 𝐵 ∣ 𝐵 ∣ 𝐵
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where the probability of both events A and B happening together is denoted by the symbol P(A∩B), and the likelihood of event B occurring is denoted by the symbol P(B) in the case of event A's occurrence.
