# 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?

- Â½ – Â½
- Â½ Ã· Â½
- Â½ + Â½
**Â½ * Â½**

## 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 investorâ€™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.

**Bayesâ€™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()*