Normal distribution in SciPy - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to import the normal distribution function from scipy.stats.

SciPy

from scipy.stats import [1]

# Now you can use norm to work with normal distribution

Drag options to blanks, or click blank then click option'

Agauss

Bnormal

Cnorm

Dstats

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'normal' instead of 'norm' which is not a valid import.

Trying to import 'gauss' which is not part of scipy.stats.

Importing 'stats' which is the module, not the distribution function.

The normal distribution function in scipy.stats is called norm. Importing it allows you to use its methods.

2fill in blank

medium

Complete the code to calculate the probability density function (PDF) of a normal distribution at x=0.

SciPy

from scipy.stats import norm

pdf_value = norm.pdf([1])
print(pdf_value)

Drag options to blanks, or click blank then click option'

A0

B1

C-1

D0.5

Attempts:

3 left

💡 Hint

Common Mistakes

Using 1 or -1 which are not the peak points of the standard normal distribution.

Using 0.5 which is arbitrary and not the peak.

The PDF of the standard normal distribution is highest at x=0, so we calculate it at 0.

3fill in blank

hard

Fix the error in the code to generate 5 random samples from a normal distribution with mean 10 and standard deviation 2.

SciPy

from scipy.stats import norm

samples = norm.rvs(loc=[1], scale=2, size=5)
print(samples)

Drag options to blanks, or click blank then click option'

A2

B0

C5

D10

Attempts:

3 left

💡 Hint

Common Mistakes

Setting loc to 2 which is the standard deviation, not the mean.

Setting loc to 0 or 5 which are incorrect for this distribution.

The loc parameter sets the mean of the normal distribution. Here, it should be 10.

4fill in blank

hard

Fill both blanks to create a dictionary comprehension that maps numbers 1 to 5 to their normal PDF values with mean 0 and std 1, but only include values where PDF is greater than 0.2.

SciPy

pdf_dict = {x: norm.pdf(x, loc=[1], scale=[2]) for x in range(1, 6) if norm.pdf(x, loc=0, scale=1) > 0.2}

Drag options to blanks, or click blank then click option'

A0

B1

C2

D5

Attempts:

3 left

💡 Hint

Common Mistakes

Using 1 for mean or 0 for std which reverses the parameters.

Using 2 or 5 which are not standard parameters.

The mean (loc) is 0 and standard deviation (scale) is 1 for the standard normal distribution.

5fill in blank

hard

Fill all three blanks to create a dictionary comprehension that maps numbers 1 to 5 to their cumulative distribution function (CDF) values for a normal distribution with mean 5 and std 2, but only include values where CDF is less than 0.8.

SciPy

cdf_dict = {x: norm.[1](x, loc=[2], scale=[3]) for x in range(1, 6) if norm.cdf(x, loc=5, scale=2) < 0.8}

Drag options to blanks, or click blank then click option'

Acdf

B5

C2

Dpdf

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'pdf' instead of 'cdf' for cumulative probabilities.

Mixing up mean and std values.

The method to get cumulative probabilities is cdf. The mean is 5 and standard deviation is 2.

Practice

1. What does the normal distribution model in data science?

easy

A. Data with no variation

B. Data with only positive values

C. Data sorted in ascending order

D. Data spread around an average value

Solution

1. Step 1: Understand the normal distribution concept

   The normal distribution describes how data points are spread around a central average (mean).

2. Step 2: Identify the correct description

   Among the options, only data spread around an average matches the normal distribution's purpose.

3. Final Answer:

   Data spread around an average value -> Option D

4. Quick Check:

   Normal distribution = data around average [OK]

Hint: Normal distribution centers data around mean [OK]

Common Mistakes:

• Thinking normal distribution only has positive values
• Confusing normal distribution with sorted data
• Assuming no variation in normal distribution

2. Which of the following is the correct way to import the normal distribution functions from scipy.stats?

easy

A. import scipy.norm

B. from scipy.stats import norm

C. from scipy import normal

D. import stats.norm

Solution

1. Step 1: Recall scipy.stats import syntax

   The normal distribution functions are in scipy.stats under the name 'norm'.

2. Step 2: Match correct import statement

   Only 'from scipy.stats import norm' correctly imports the normal distribution functions.

3. Final Answer:

   from scipy.stats import norm -> Option B

4. Quick Check:

   Correct import = from scipy.stats import norm [OK]

Hint: Use 'from scipy.stats import norm' to access normal distribution [OK]

Common Mistakes:

• Using 'import scipy.norm' which does not exist
• Trying 'from scipy import normal' which is incorrect
• Importing 'stats.norm' without scipy prefix

3. What is the output of this code?

from scipy.stats import norm
result = norm.cdf(0, loc=0, scale=1)
print(round(result, 2))

medium

A. 1.00

B. 0.00

C. 0.50

D. 0.84

Solution

1. Step 1: Understand norm.cdf at mean

   norm.cdf(x, loc, scale) gives the probability data is less than x. At x=0 with mean=0, scale=1, it is the 50th percentile.

2. Step 2: Calculate and round the result

   The cumulative probability at mean is 0.5, rounding to 2 decimals gives 0.50.

3. Final Answer:

   0.50 -> Option C

4. Quick Check:

   norm.cdf(mean) = 0.5 [OK]

Hint: CDF at mean of normal = 0.5 [OK]

Common Mistakes:

• Confusing PDF with CDF values
• Expecting 0 or 1 instead of 0.5 at mean
• Rounding errors ignoring decimals

4. Find the error in this code snippet:

from scipy.stats import norm
prob = norm.pdf(1, mean=0, scale=1)
print(prob)

medium

A. Parameter 'mean' should be 'loc'

B. Missing import statement

C. norm.pdf does not exist

D. scale must be an integer

Solution

1. Step 1: Check parameter names for norm.pdf

   norm.pdf uses 'loc' for mean, not 'mean'. Using 'mean' causes an error.

2. Step 2: Identify correct parameter

   Replace 'mean=0' with 'loc=0' to fix the code.

3. Final Answer:

   Parameter 'mean' should be 'loc' -> Option A

4. Quick Check:

   Use loc for mean in norm functions [OK]

Hint: Use 'loc' not 'mean' for normal distribution mean [OK]

Common Mistakes:

• Using 'mean' instead of 'loc' parameter
• Assuming norm.pdf is missing
• Thinking scale must be integer

5. You want to find the probability that a value from a normal distribution with mean 10 and standard deviation 2 is less than 13. Which code correctly calculates this using scipy?

hard

A. norm.cdf(13, loc=10, scale=2)

B. norm.pdf(13, loc=10, scale=2)

C. norm.cdf(10, loc=13, scale=2)

D. norm.sf(13, loc=10, scale=2)

Solution

1. Step 1: Identify the function for cumulative probability

   To find probability less than a value, use norm.cdf with the value, mean (loc), and std dev (scale).

2. Step 2: Match parameters to the problem

   Value is 13, mean is 10, std dev is 2, so norm.cdf(13, loc=10, scale=2) is correct.

3. Final Answer:

   norm.cdf(13, loc=10, scale=2) -> Option A

4. Quick Check:

   Use norm.cdf(value, loc=mean, scale=std) [OK]

Hint: Use norm.cdf for probability less than a value [OK]

Common Mistakes:

• Using norm.pdf instead of norm.cdf
• Swapping loc and value parameters
• Using norm.sf which gives probability greater than value