Week 5 - Continuous Probability Distributions

Question 1

What do we use when dealing with continuous variables?

Answer 1

probability density function

Question 2

possible mid makeup question

What is a normal distribution?

Answer 2

The probability distribution for a continuous random variable that meets these criteria:
* The graphed curve of the distribution is bell-shaped and symmetrical.
* The mean, median, and mode are all the same value.
* The population mean 𝜇 and the population standard deviation 𝜎 determine probabilities.
* The distribution has an inifinite range
* Probabilities are always cumulative and expressed as inequalities, such as P < X or P ≥ X.

Question 3

What are the properties of the normal curve?

Answer 3

1. the mode occurs at x=𝜇
2. the curve is symmetric about a vertical axis
3. concave downward if μ −σ < x < μ+ σ and is concave upward otherwise (these are inflection points)
4. the total area under the curve and above the horizontal axis is equal to 1

(there is one more, but i’ll never remember it so who gives a fuck)

Question 4

How do you calculate the Z score?

Answer 4

Z = (x- μ) / σ

Z - standard score
x - observed value
μ - mean
σ - standard deviation

Question 5

What is a Z score?

Answer 5

A Z Score (Standard Score) is a measurement of how many standard deviations below or above the population mean that score is.

We use it to compare results to the normal population or mean.

Which means that if Z Score = 1 then that value is one standard deviation from the
mean. Whereas if Z Score = 0, it means the value is identical to the mean.

Could be positive (above the mean) and negative (below the mean).