Continuous, Probability and Distributions

Question 1

A PDF is?

Answer 1

A probability distribution function, with a graph that has a definite integral of 1

(from a to b)

Question 2

How do you find the CDF?

Answer 2

A cumulative distribution function, with a PDF graph that has a definite integral from a to x (where a is the first value)

Question 3

Quantiles can be found by?

Answer 3

CDF = whatever value (in decimal form)

e.g.
3rd quartile, CDF = 0.75
6th decile, CDF = 0.6
37th percentile, CDF = 0.37

Question 4

What is a normal distribution?

Answer 4

PDF that looks is symmetrical and looks like a bell, hence its other name the ‘bell curve’

Question 5

How is a normal distribution arranged?

Answer 5

In the middle is the median, mean and mode (μ) and from there it goes out ±1σ, ±2σ, ±3σ

Question 6

What does a STANDARD normal distribution have for its values of μ and σ?

Answer 6

μ = 0
σ = 1

Question 7

Empirical Rule states that?

Answer 7

On a normal distribution:
The values between ±1σ, will represent 68% of the data
The values between ±2σ, will represent 95% of the data
The values between ±3σ, will represent 99.7% of the data

Question 8

How do you find the z score, and what does a z score do?

Answer 8

z = (x - μ)/σ

Tells you how many standard deviations σ you are away from the mean μ

Question 9

What is the method for finding probability of data on a normal distribution?
1. First step?

Answer 9

Find the z score, approximate to 2 decimals

Question 10

What is the method for finding probability of data on a normal distribution?
2. Second step?

Answer 10

Check the table for the t-score:
If it’s less than → straight to the t-score
If it’s greater than → 1 minus the t-score
If it’s between → bigger t-score minus the smaller t-score

note table is in page 633-34

Question 11

What do you want if x is above the mean?

Answer 11

Bigger z score so you can significantly outrank mediocrity

Question 12

What do you want if x is below the mean?

Answer 12

Smaller z score so you can significantly outrank complete failure

Question 13

How do you draw on data onto a normal distribution?

1. First step?

Answer 13

Change to decimals

e.g. If question says value between bottom 10% and top 40% on standard dis table
bottom 10% = 0.1
top 40% = 60% = 0.6

Question 14

How do you draw on data onto a normal distribution?

2. Second step?

Answer 14

Reverse engineer, look for at t-score FOR z score

e.g. If question says value between bottom 10% and top 40% on standard dis table
t1 = 0.1 → z1 ≈ 1.285
t2 = 0.6 → z2 ≈ 0.265

Question 15

How do you draw on data onto a normal distribution?

3. Third step?

Answer 15

Place onto PDF for x-values

e.g. If question says value between bottom 10% and top 40% on standard dis table
z1 ≈ 1.285 → x1 ≈ 1.285
z2 ≈ 0.265 → x2 ≈ 0.265