Computer Prac - Normal Distribution

Question 1

What is normal distribution?

Answer 1

The most common of all of the distributions that you may see concerning the way data are distributed.
BELL SHAPE
Known as the “Gaussian” after Frederic Gauss.
Most commonly used frequency/graph.
eg heights in a population.
It is always an approximation and needs to be evaluation.

Question 2

How is the normal deviation defined?

Answer 2

It is defined by: 
the mean (u) the centre of the distribution
and the standard deviation (o) the width of the deviation.

Question 3

What is the STANDARD normal deviation?

Answer 3

All NORMAL distributions are the same shape.
The STANDARD deviation is a special case.
It has a mean of zero and standard deviation of 1.

Question 4

1. The normal distribution can be left- or right-skewed depending on its parameters.
2. A normal distribution is always symmetric, unimodal, and bell-shaped.

Answer 4

1. False

2. True

Question 5

A normal distribution is always symmetric, unimodal, and bell-shaped. True or false.

Answer 5

True

Question 6

1. When plotted on the same scale, N(μ=1,σ=2) is wider than N(μ=1,σ=1).
   OR
2. When plotted on the same scale, N(μ=1,σ=1) is narrower than (Nμ=1,σ=2).
   OR
3. When plotted on the same scale N (u=1, o=2) is narrower than N (u=1, o=1)

Answer 6

1. true
2. true
3. false

Question 7

An observation equal to the mean is always at the 0.
OR
An observation equal to the mean is always at the 50th percentile.

Answer 7

1. False

2. True

Question 8

1. The Z-score of an observation is defined as the number of standard deviations it falls above or below the mean.
   OR
2. An observation with a positive Z-score is always more unusual than an observation with a negative Z-score.
   OR
3. The absolute value of an observation’s Z-score quantifies how unusual the observation is.
   OR
4. A Z-score of 0 always corresponds to an observation equal to the mean.
5. The z score of an observation can never be 0.

Answer 8

1. True
2. False
3. True
4. True
5. False

Question 9

A normal distribution is always symmetric, unimodal, and bell-shaped. True or false.

Answer 9

True

Question 10

A normal distribution always has mean μ=0 and standard deviation σ=1.
OR
A normal distribution is symmetrical as long as μ=0.n
T or F.

Answer 10

BOTH FALSE

μ = the centre of the distribution
σ = width of the distribution

The STANDARD (not normal )normal distribution always has mean μ=0 and standard deviation σ=1.

Question 11

A normal distribution is symmetrical as long as μ=0.n

T or F.

Answer 11

False

Question 12

The standard normal distribution always has mean μ=0 and standard deviation σ=1.

Answer 12

True

Question 13

A Z-score of 0 always corresponds to an observation equal to the mean. True or false.

Answer 13

True

Question 14

The percentile of an observation corresponds to the percentage of observations that are smaller than it.

Answer 14

True

Question 15

1. The probability of a random observation falling within 3 standard deviations of the mean is roughly 95%.
2. The probability of a random observation falling within 2 standard lpdeviations of the mean is roughly 95%

Answer 15

1. False

2. True