Week 5: Probability Distribution

Question 1

To determine whether a dataset follows a ‘normal distribution’ we can employ several methods what are they?

Answer 1

1. Histogram and density curve
2. Empirical Rule Intervals
3. IQR to SD ratio

Question 2

What does it mean if we use empirical rule to see if it follows a ‘normal distribution’?

Answer 2

We calculate the intervals of

µ ± σ, µ ± 2σ, and µ ± 3σ, and determine
the percentage of data points within each

For a normal distribution it would follow a 68, 95,99 range

Question 3

What is the histogram ad density curve

Answer 3

Its when we construct a histogram and overlay it with a density curve

A normal distribution is symmetric around the mean.

Question 4

What does it mean if we use IQR to SD ratio’ rule to see if it follows a ‘normal distribution’?

Answer 4

Find the IQR and SD , then calculate the ratio IRQ/Sd

In a normal distribution this ratio would be around 1.3

Question 5

For IQR to SD ratio what if the ratio does not follow a ‘standard normal distribution’ what do we do?

Answer 5

standardize the ratio

QU =XU − µ/ σ
QL =XL − µ/σ

Hence, XU = QU σ + µ and XL = QL σ + µ

Remember here you would fid the z-scores correspondent to it