Normal distribution with normal() in NumPy - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does the numpy.random.normal() function do?

It generates random numbers that follow a normal (bell-shaped) distribution, centered around a mean value with a given spread (standard deviation).

beginner

What are the main parameters of numpy.random.normal()?

The main parameters are loc (mean), scale (standard deviation), and size (number of values to generate).

beginner

Why is the standard deviation important in a normal distribution?

Standard deviation controls how spread out the numbers are around the mean. A small value means numbers are close to the mean; a large value means they are more spread out.

beginner

How can you generate 1000 random numbers with mean 10 and standard deviation 2 using numpy?

Use numpy.random.normal(loc=10, scale=2, size=1000) to get 1000 numbers centered at 10 with spread 2.

intermediate

What shape of data does numpy.random.normal() return when size is a tuple?

It returns a NumPy array with the shape given by the tuple, filled with random numbers from the normal distribution.

What does the loc parameter in numpy.random.normal() specify?

A The number of samples to generate

B The mean of the distribution

C The standard deviation of the distribution

D The minimum value of the distribution

loc sets the center (mean) of the normal distribution.

If you want to generate 500 random numbers from a normal distribution, which parameter controls this?

A loc

B scale

C size

D mean

size controls how many random numbers are generated.

What happens if you set scale=0 in numpy.random.normal()?

A You get random numbers spread out widely

B You get negative numbers only

C You get an error

D You get all numbers equal to the mean

With zero standard deviation, all values equal the mean.

Which shape will the output have if you use size=(3,4)?

A A 3 by 4 NumPy array

B A list of 12 numbers

C A single number

D A 4 by 3 NumPy array

The output shape matches the size tuple, so 3 rows and 4 columns.

Which of these is true about the normal distribution?

A It is symmetric around the mean

B It has no mean

C It only produces positive numbers

D It is always skewed to the right

The normal distribution is symmetric around its mean.

Explain how to use numpy.random.normal() to simulate real-world data like heights or test scores.

Think about how average and spread describe real data.

Describe the effect of changing the scale parameter on the shape of the data generated by numpy.random.normal().

Consider what happens when spread increases or decreases.

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()