the power of statistics coursera weekly challenge 2 answers

Test your knowledge: Basic concepts of probability

1. Objective probability is based on personal feeling, experience, or judgment.

  • True
  • False

2. Fill in the blank: In statistics, a number between _____ is used to express the probability that an event will occur.

  • -1 and 1
  • -1 and 0
  • 0 and 1
  • 1 and 2

3. The probability of no snow tomorrow equals 1 minus the probability of snow tomorrow. This is an example of what rule of probability?

  • Multiplication rule
  • Division rule
  • Addition rule
  • Complement rule

Test your knowledge: Conditional probability

4. What is conditional probability?

  • The probability of a single random event occurring
  • The probability of two events occurring at the same time
  • The probability of an event occurring given that another event has already occurred
  • The probability of a highly unlikely event occurring

5. Suppose two events occur: The first event is drawing an ace from a standard deck of playing cards, and the second event is drawing another ace from the same deck. What term is used to describe these two events?

  • Subjective
  • Objective
  • Independent
  • Dependent

6. Fill in the blank: _____ probability is the updated probability of an event based on new data.

  • Prior
  • Posterior
  • Empirical
  • Classical

Test your knowledge: Discrete probability distributions

7. Which of the following statements describe continuous random variables? Select all that apply.

  • Continuous random variables take all the possible values in some range of numbers.
  • Continuous random variables are typically whole numbers.
  • Continuous random variables are typically negative numbers;
  • Continuous random variables are typically decimal values.

8. What probability distribution represents experiments with repeated trials that each have two possible outcomes: success or failure?

  • The binomial distribution
  • The normal distribution
  • The trinomial distribution
  • The Poisson distribution

Test your knowledge: Continuous probability distributions

9. The normal distribution has which of the following features? Select all that apply.

  • The curve is symmetrical on both sides of the center
  • The total area under the curve equals 4
  • The shape is a bell curve
  • The mean is located at the center of the curve

10. What does the empirical rule state?

  • For a dataset with a normal distribution, 33.3% of values fall within 1 standard deviation of the mean, 33.3% of values fall within 2 standard deviations of the mean, and 33.3% of values fall within 3 standard deviations of the mean.
  • For a dataset with a normal distribution, 68% of values fall within 1 standard deviation of the mean, 95% of values fall within 2 standard deviations of the mean, and 99.7% of values fall within 3 standard deviations of the mean.
  • For a dataset with a normal distribution, 100% of values fall within 1 standard deviation of the mean.
  • For a dataset with a normal distribution, 50% of values fall within 1 standard deviation of the mean, 30% of values fall within 2 standard deviations of the mean, and 20% of values fall within 3 standard deviations of the mean.

11. A data value is 2 standard deviations above the mean. What is its z-score?

  • -2
  • 0
  • 2
  • 1

Test your knowledge: Probability distributions with Python

12. A data professional is working with a dataset that has a normal distribution. To test out the empirical rule, they want to find out if roughly 68% of the data values fall within 1 standard deviation of the mean. What Python functions will enable them to compute the mean and standard deviation?

  • mn() and std()
  • mean() and std()
  • mn() and stand()
  • mean() and standard()

13. What Python function is used to compute z-scores for data?

  • normal.zscore()
  • stats.zscore()
  • mean.zscore()
  • median.zscore()

Weekly challenge 2

14. 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?

  • Independent
  • Objective
  • Dependent
  • Subjective

15. 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 likely to occur.
  • The event is certain to occur.
  • The event is certain not to occur.
  • The event is unlikely to occur.

16. The probability of rain tomorrow is 40%. What is the probability of the complement of this event?

  • The probability of no rain tomorrow is 60%.
  • The probability of no rain tomorrow is 40%.
  • The probability of no rain tomorrow is 20%.
  • The probability of no rain tomorrow is 80%.

17. A first coin toss results in tails, and a second coin toss results in heads. What concept best describes these two events?

  • Non-random
  • Subjective
  • Dependent
  • Independent

18. What concept refers to the probability of an event before new data is collected?

  • Posterior probability
  • Conditional probability
  • Subjective probability
  • Prior probability

19. Which of the following statements accurately describes a key difference between discrete and continuous random variables?

  • Discrete random variables are negative numbers; continuous random variables are positive numbers.
  • Discrete random variables are positive numbers; continuous random variables are negative numbers.
  • 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.

20. Fill in the blank: The _____ distribution best models the number of heads in 10 fair coin flips.

  • Normal
  • Bernoulli
  • Poisson
  • Binomial

21. 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?

  • 99.7%
  • 50%
  • 95%
  • 68%

22. If a data value has a z-score of 0, what does the value equal?

  • The mode
  • The mean
  • The median
  • The standard deviation

23. 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?

  • median.zscore()
  • mean.zscore()
  • stats.zscore()
  • normal.zscore()

24. If all outcomes of an event are equally likely, how is its probability calculated?

  • 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 number of desired outcomes by the total number of possible outcomes.
  • Divide the total number of possible outcomes by the number of certain outcomes.

25. A coin is tossed twice. To calculate the probability of getting two heads in a row, which of the following equations should be used?

  • ½ – ½
  • ½ ÷ ½
  • ½ + ½
  • ½ * ½

26. Which of the following events are mutually exclusive? Select all that apply.

  • 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 heads on a first coin toss and tails on a second coin toss
  • Getting a 4 and a 6 on the same die roll

27. Which of the following are examples of discrete random variables? Select all that apply.

  • The number of radios produced in a factory each day
  • The time it takes to drive from one city to another city
  • The number of rooms in a hotel
  • The length of an airplane

28. The Poisson distribution can model which of the following kinds of data? Select all that apply.

  • The number of visitors per day on a website
  • The number of heads in 10 fair coin tosses
  • The number of customers per week at a retail store
  • The number of calls per hour at a call center

29. 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?

  • 130g
  • 160g
  • 180g
  • 120g

30. The mean and the standard deviation of a standard normal distribution always equal what values?

  • Mean = 1; standard deviation = 2
  • Mean = 2; standard deviation = 1
  • Mean = 0; standard deviation = 2
  • Mean = 0; standard deviation = 1

31. An investor believes there is a 90% chance that the price of a certain stock will increase in the next year. The investor’s prediction is based exclusively on intuition. What type of probability are they using?

  • Empirical
  • Objective
  • Subjective
  • Classical

32. A jar contains four marbles: Two marbles are red, one is green, and one is blue. One marble is taken from the jar. What is the probability that the marble is blue?

  • 100%
  • 50%
  • 25%
  • 75%

33. Fill in the blank: To calculate posterior probability, a data professional can use _____ to update the prior probability based on the data.

  • Bayes’s theorem
  • the binomial distribution
  • the normal distribution
  • the complement rule

34. Which of the following are examples of continuous random variables? Select all that apply.

  • The time it takes for a person to run a race
  • The height of a redwood tree
  • The number of students in a math class
  • The weight of a polar bear

35. A data professional working for a smartphone manufacturer is analyzing sample data on the weight of a smartphone. The data follows a normal distribution, with a mean weight of 150g and a standard deviation of 10g. What data value lies at the center of the distribution curve?

  • 150g
  • 10g
  • 160g
  • 140g

36. A data professional might use the Python function stats.zscore() to help them do which of the following? Select all that apply.

  • Plot a histogram
  • Simulate taking a random sample of data
  • Compute z-scores for their data
  • Detect outliers in their data

37. Fill in the blank: The Python function _____ enables data professionals to compute z-scores for their data.

  • normal.zscore()
  • var()
  • describe()
  • stats.zscore()

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