M14: Continuous Probability Distributions

Question 1

Random variable

Answer 1

Numerical measurement of the outcome of a random phenomenon

Question 2

Parameters

Answer 2

a) mu - Population mean
b) Sigma - Population STDV

Question 3

Continuous random variable

Answer 3

One that has an infinite number of possible outcomes

Question 4

Smooth curve (Distribution) and Probabilities

Answer 4

Smoothed out histogram
a) Probabilities can be represented as areas under a density curve
b) Total area = 1

Question 5

What is the probability of a specific outcome?

Answer 5

Each outcome has a zero probability of happening, but we can assign probabilities to intervals

Question 6

Features of normal distribution

Answer 6

a) Bell-shaped
b) Symmetric
c) Centered at their mean with standard deviation

Question 7

Notation

Answer 7

X~N(mean, stdv)

Question 8

Empirical rule (Proportions)

Answer 8

a) 68% within 1 stdv
b) 95% within 2 stdv
c) 99.7% within 3 stdv

Question 9

Standardized observations (Z-scores)

Answer 9

z = (x - mean) / stdv

Question 10

What does the z-score tell you?

Answer 10

How many STDV above or below the mean an observation x is

Question 11

Standard normal distribution

Answer 11

Z ~ N(0,1)