Normal distribution in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Normal Distribution PDF Calculation

What is the output of this code that calculates the probability density function (PDF) of a normal distribution at x=0 with mean=0 and standard deviation=1?

SciPy

from scipy.stats import norm
result = norm.pdf(0, loc=0, scale=1)
print(round(result, 4))

A 0.5000

B 0.3989

C 1.0000

D 0.0000

💡 Hint

Recall the formula for the normal distribution PDF at the mean.

The PDF of a standard normal distribution at its mean (0) is 1 divided by the square root of 2π, approximately 0.3989.

❓ data_output

intermediate

Number of Samples within One Standard Deviation

Using scipy, generate 1000 samples from a normal distribution with mean=5 and std=2. How many samples fall between 3 and 7 (within one standard deviation)?

SciPy

import numpy as np
from scipy.stats import norm
samples = norm.rvs(loc=5, scale=2, size=1000, random_state=42)
count = np.sum((samples >= 3) & (samples <= 7))
print(count)

A 950

B 500

C 682

D 840

💡 Hint

Recall the empirical rule for normal distributions.

About 68% of data in a normal distribution lies within one standard deviation from the mean. 68% of 1000 is about 680.

❓ visualization

advanced

Plotting Normal Distribution PDF with Different Parameters

Which option produces a plot showing two normal distribution curves: one with mean=0, std=1 and another with mean=2, std=0.5?

SciPy

import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import norm
x = np.linspace(-3, 5, 500)
plt.plot(x, norm.pdf(x, 0, 1), label='mean=0, std=1')
plt.plot(x, norm.pdf(x, 2, 0.5), label='mean=2, std=0.5')
plt.legend()
plt.show()

A Plots two curves: a wider bell centered at 0 and a narrower bell centered at 2

B Plots two identical curves both centered at 0

C Plots one curve only centered at 1

D Raises a TypeError due to wrong function usage

💡 Hint

Check the parameters passed to norm.pdf for each curve.

The code plots two normal PDFs with different means and std deviations, resulting in two distinct bell curves.

🧠 Conceptual

advanced

Understanding the Effect of Standard Deviation on Normal Distribution Shape

Which statement correctly describes how increasing the standard deviation affects the shape of a normal distribution?

A The curve becomes wider and shorter, spreading data over a larger range

B The curve becomes narrower and taller, concentrating data near the mean

C The curve shifts to the right without changing shape

D The curve becomes asymmetric, skewing to one side

💡 Hint

Think about how spread relates to standard deviation.

Increasing standard deviation spreads data out, making the bell curve wider and lower in height.

🔧 Debug

expert

Identify the Error in Normal Distribution Sampling Code

What error does this code raise when trying to generate samples from a normal distribution? import numpy as np from scipy.stats import norm samples = norm.rvs(loc=0, scale=-1, size=100) print(samples)

SciPy

import numpy as np
from scipy.stats import norm
samples = norm.rvs(loc=0, scale=-1, size=100)
print(samples)

A RuntimeWarning: invalid value encountered in sqrt

B No error, prints 100 samples

C TypeError: unsupported operand type(s) for -: 'int' and 'str'

D ValueError: scale parameter must be positive

💡 Hint

Check the scale parameter value passed to norm.rvs.

The scale (standard deviation) must be positive. Negative scale causes ValueError.