Normal distribution with normal() in NumPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of numpy normal() with fixed seed

What is the output of this code snippet that generates 3 random numbers from a normal distribution with mean 0 and standard deviation 1?

NumPy

import numpy as np
np.random.seed(0)
samples = np.random.normal(0, 1, 3)
print(samples)

A [0.49671415 -0.1382643 0.64768854]

B [1.76405235 0.40015721 0.97873798]

C [ 0.76103773 0.12167502 0.44386323]

D [ 1.86755799 -0.97727788 0.95008842]

💡 Hint

Remember to set the random seed before generating samples to get reproducible results.

Setting np.random.seed(0) fixes the random number generator state. The first three samples from np.random.normal(0,1,3) with this seed are [1.76405235, 0.40015721, 0.97873798].

❓ data_output

intermediate

Shape of output array from normal()

What is the shape of the array produced by this code?

NumPy

import numpy as np
result = np.random.normal(loc=5, scale=2, size=(4,3))
print(result.shape)

A (4, 3)

B (4,)

C (12,)

D (3, 4)

💡 Hint

The size parameter defines the shape of the output array.

The size=(4,3) argument tells numpy to generate a 2D array with 4 rows and 3 columns, so the shape is (4, 3).

❓ visualization

advanced

Histogram of samples from normal distribution

Which option shows the correct histogram plot code for 1000 samples from a normal distribution with mean 0 and standard deviation 1?

NumPy

import numpy as np
import matplotlib.pyplot as plt
samples = np.random.normal(0, 1, 1000)
# Fill in the code to plot histogram

A

plt.bar(range(30), samples[:30])
plt.title('Bar plot of first 30 samples')
plt.show()

B

plt.plot(samples)
plt.title('Line plot of samples')
plt.show()

C

plt.scatter(range(1000), samples)
plt.title('Scatter plot of samples')
plt.show()

D

plt.hist(samples, bins=30, color='blue', edgecolor='black')
plt.title('Histogram of Normal Samples')
plt.show()

💡 Hint

Histograms show frequency distribution of data values.

Option D correctly uses plt.hist() to plot the frequency distribution of the 1000 samples with 30 bins, which is the standard way to visualize a normal distribution sample.

🧠 Conceptual

advanced

Effect of scale parameter in normal()

What happens to the spread of data when you increase the scale parameter in np.random.normal(loc=0, scale=scale_value, size=1000)?

A The data points become more concentrated around the mean, decreasing the standard deviation.

B The mean of the data shifts to the scale value.

C The data points become more spread out, increasing the standard deviation.

D The number of data points generated increases.

💡 Hint

Scale is the standard deviation of the normal distribution.

The scale parameter controls the standard deviation. Increasing it makes the data spread wider around the mean.

🔧 Debug

expert

Identify error in normal() usage

What error will this code raise and why? import numpy as np samples = np.random.normal(0, -1, 5) print(samples)

NumPy

import numpy as np
samples = np.random.normal(0, -1, 5)
print(samples)

A ValueError: scale < 0

B TypeError: loc must be a float

C SyntaxError: invalid syntax

D No error, prints 5 samples

💡 Hint

Scale (standard deviation) must be positive.

The scale parameter cannot be negative. Passing -1 causes numpy to raise a ValueError indicating scale must be non-negative.

Practice

1. What does the loc parameter control in the numpy.random.normal() function?

easy

A. The spread (standard deviation) of the normal distribution

B. The center (mean) of the normal distribution

C. The number of random values generated

D. The shape of the distribution curve

Solution

1. Step 1: Understand the parameters of normal()

   The normal() function has parameters loc and scale. loc sets the mean (center) of the distribution.

2. Step 2: Identify the role of loc

   The mean is the center point where most values cluster in a bell curve.

3. Final Answer:

   The center (mean) of the normal distribution -> Option B

4. Quick Check:

   loc = center [OK]

Hint: Remember: loc = center, scale = spread [OK]

Common Mistakes:

• Confusing loc with scale
• Thinking loc controls number of samples
• Assuming loc changes distribution shape

2. Which of the following is the correct syntax to generate 5 random numbers from a normal distribution with mean 10 and standard deviation 2 using numpy?

easy

A. numpy.random.normal(size=5, mean=10, std=2)

B. numpy.normal(10, 2, 5)

C. numpy.random.normal(5, loc=10, scale=2)

D. numpy.random.normal(loc=10, scale=2, size=5)

Solution

1. Step 1: Recall the correct function and parameters

   The function is numpy.random.normal() with parameters loc for mean, scale for std dev, and size for number of samples.

2. Step 2: Match parameters to correct syntax

   numpy.random.normal(loc=10, scale=2, size=5) correctly uses loc=10, scale=2, and size=5.

3. Final Answer:

   numpy.random.normal(loc=10, scale=2, size=5) -> Option D

4. Quick Check:

   Correct parameter names and order [OK]

Hint: Use loc=mean, scale=std, size=number [OK]

Common Mistakes:

• Using wrong parameter names like mean or std
• Mixing order without keywords
• Calling numpy.normal instead of numpy.random.normal

3. What is the output shape of the following code?

import numpy as np
arr = np.random.normal(loc=0, scale=1, size=(3,4))
print(arr.shape)

medium

A. (12,)

B. (4, 3)

C. (3, 4)

D. (3,)

Solution

1. Step 1: Understand the size parameter

   The size argument is set to (3,4), which means generate a 2D array with 3 rows and 4 columns.

2. Step 2: Check the shape of the generated array

   Printing arr.shape returns the shape tuple, which matches the size argument.

3. Final Answer:

   (3, 4) -> Option C

4. Quick Check:

   size=(3,4) means shape=(3,4) [OK]

Hint: size tuple = output shape [OK]

Common Mistakes:

• Confusing rows and columns order
• Expecting flattened array shape
• Ignoring tuple format for size

4. Identify the error in this code snippet:

import numpy as np
samples = np.random.normal(mean=0, std=1, size=10)
print(samples)

medium

A. Incorrect parameter names: should use loc and scale instead of mean and std

B. Missing import statement for numpy

C. size parameter must be a tuple, not an integer

D. The print statement syntax is wrong

Solution

1. Step 1: Check parameter names for normal()

   The function np.random.normal() expects loc for mean and scale for standard deviation, not mean or std.

2. Step 2: Verify other parts of the code

   Import is correct, size can be integer, and print syntax is valid.

3. Final Answer:

   Incorrect parameter names: should use loc and scale instead of mean and std -> Option A

4. Quick Check:

   Use loc and scale for mean and std [OK]

Hint: Use loc=mean, scale=std; mean/std are invalid [OK]

Common Mistakes:

• Using mean or std instead of loc and scale
• Thinking size must be tuple always
• Assuming print syntax error

5. You want to simulate daily temperatures for a week that average 20°C with a standard deviation of 3°C. Which code correctly generates this data and calculates the average temperature?

hard

A. temps = np.random.normal(loc=20, scale=3, size=7)
avg_temp = temps.mean()
print(round(avg_temp, 2))

B. temps = np.random.normal(mean=20, std=3, size=7)
avg_temp = temps.sum()
print(avg_temp)

C. temps = np.random.normal(loc=3, scale=20, size=7)
avg_temp = temps.mean()
print(avg_temp)

D. temps = np.random.normal(loc=20, scale=3, size=7)
avg_temp = temps.median()
print(avg_temp)

Solution

1. Step 1: Generate temperatures with correct parameters

   Use loc=20 for mean temperature and scale=3 for standard deviation, with size=7 for a week.

2. Step 2: Calculate the average temperature correctly

   Use temps.mean() to get the average. Round for neat output.

3. Final Answer:

   temps = np.random.normal(loc=20, scale=3, size=7) avg_temp = temps.mean() print(round(avg_temp, 2)) -> Option A

4. Quick Check:

   loc=mean, scale=std, mean() for average [OK]

Hint: Use loc=mean, scale=std, mean() to average [OK]

Common Mistakes:

• Swapping loc and scale values
• Using mean or std instead of loc and scale
• Using sum() instead of mean() for average
• Using median() instead of mean()