Normal distribution and continuous random variable

Normal distribution and continuous random variable

Lessons

• Introduction

$\cdot$ Why are z-scores needed for random continuous variables?
$\cdot$ Relationship between area under the curve and probability
$\cdot$ Leads to Standard normal distribution

• 1.
Use the Z table to find:
a)
the z-score when the area under the curve to the left of z is 0.3015.

b)
the area from the mean to a z-score of 1.45.

c)
the z-score when the area under the curve to the left of z is 0.7774.

• 2.
Finding Probabilities from Z-Scores
Answer the following questions based on the properties of standard normal distribution.
a)
What is the probability of having a z-score that is less than 0.75?

b)
What is the probability of having a z-score that is greater than -1.83?

c)
What is the probability of having a z-score that is between -1.27 to 1.06?

• 3.
Finding Z-Scores from Areas
Answer the following questions based on the properties of standard normal distribution.
i) by Z table
ii) by calculator
a)
Find the z-score that represents the bottom 70%.

b)
Find the z-score that represent the top 70%.

c)
Find the z-scores that represent the top 4% and the bottom 4%.