Week 4: Probability Distribution

Question 1

What two characteristics does a normal distribution have?

Answer 1

1. Mean
2. Sd

Question 2

What does a density curve look like when it follows a normal distribution?

Answer 2

Its symmetric around the mean and is spread out by its s.

Question 3

What is the purpose of the density curve

Answer 3

To see the relative likelihood for a specific x value

Question 4

What is the probability of a continuous probability distribution

Answer 4

Its ZERO

Question 5

What is more meaningful to look at for probability?

Answer 5

For a continuous variable its more meaningful to discuss a value falling within a specific range of an interval that is under the probability density curve.

Question 6

What is a standard normal distribution?

Answer 6

When the
1. Mean = 0
2. SD = 1

We often see it as Z ∼ N(0, 1)

Question 7

What if a random variable follows a STANDARD normal distribution?

Answer 7

We have to use a z-table to find the probability of that specific random variable

Question 8

Ex: Pr( Z < 0.55)

Answer 8

Go to Z-table

Question 9

Example: Pr (−0.55 < Z < 0.55)

Answer 9

Pr(−0.55 < Z < 0.55) =

Pr(Z < 0.55) − Pr(Z < −0.55)
0.7088 − 0.2912 = 0.4176 (41.76%)

Question 10

Can we make a ‘general normal distribution’ into a “standard normal distribution”

Answer 10

We can and the process is called ‘standardization’

Question 11

What is the process of standardization?

Answer 11

Z =
X − µ/ σ

Then once you get the value you go to the ‘Z-table’

Question 12

pr |z| > 0.55

Answer 12

=Pr(Z > 0.55)+ Pr(Z < −0.55)

Question 13

Pr(|Z| < 0.55)

Answer 13

=Pr(Z < 0.55)- Pr(Z < −0.55)