6 Normal Distribution

Question 1

What shape does a normal distribution curve have?

Answer 1

Bell shaped

The normal distribution is characterized by its symmetrical bell shape.

Question 2

Define a continuous random variable.

Answer 2

A variable that can take any value within a given range

Continuous random variables are often used in statistics to represent measurements.

Question 3

What is the mean in a normal distribution?

Answer 3

It is the central point around which the data is distributed.

Question 4

What does the standard deviation indicate in a normal distribution?

Answer 4

The spread of the data around the mean

A larger standard deviation indicates more variability in the data.

Question 5

True or false: The total area under a normal distribution curve is 1.

Answer 5

TRUE

This property is fundamental to probability distributions.

Question 6

What percentage of data lies within one standard deviation of the mean in a normal distribution?

Answer 6

About 2/3 (~68%)

Question 7

What percentage of data lies within two standard deviations of the mean in a normal distribution?

Answer 7

95%

This property helps in understanding the spread of data.

Question 8

What percentage of data lies within three standard deviations of the mean in a normal distribution?

Answer 8

99.8%

This indicates that almost all data points fall within this range.

Question 9

The normal distribution is also known as the ____ ___.

Answer 9

Gaussian distribution

Named after the mathematician Carl Friedrich Gauss.

Question 10

What is the parameter for population mean in a normal distribution?

Answer 10

μ

This symbol represents the average of the population.

Question 11

What is the parameter for population variance in a normal distribution?

Answer 11

σ²

This symbol represents the variance of the population.

Question 12

What is the standard normal distribution?

Answer 12

A normal distribution with mean 0 and standard deviation 1

It is used for standardizing values.

Question 13

Fill in the blank: The inverse normal distribution is used to calculate the value which satisfies a given _______.

Answer 13

probability

This process is often used in statistical analysis.

Question 14

What is the continuity correction when approximating a binomial distribution with a normal distribution?

Answer 14

Adjusting for the difference between discrete and continuous data

This ensures more accurate probability calculations.

Question 15

What are the two conditions under which the normal distribution may be used as an approximation to the binomial distribution?

Answer 15

np>10 and
n(1-p)>10

These conditions help ensure the approximation is valid.

Question 16

What does the bell shape of the normal distribution indicate?

Answer 16

Symmetry around the mean

This symmetry is a key characteristic of the normal distribution.

Question 17

Fill in the blank: For the normal distribution, the mean and variance are known as the _______.

Answer 17

Parameters

Question 18

What is the mean of the standard normal distribution, Z?

Answer 18

0

Question 19

What is the standard deviation of the standard normal distribution, Z?

Answer 19

1

Question 20

What are the characteristics of the normally distributed curve?

Answer 20

Symmetrical
Continuous
Mode= median= mean
Total area under curve = 1