Normal distribution and continuous random variable

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

Reading the Z Table
Use the Z table to find:
1. the z-score when the area under the curve to the left of z is 0.3015.
2. the area from the mean to a z-score of 1.45.
3. the z-score when the area under the curve to the left of z is 0.7774.
Finding Probabilities from Z-Scores
Answer the following questions based on the properties of standard normal distribution.
1. What is the probability of having a z-score that is less than 0.75?
2. What is the probability of having a z-score that is greater than -1.83?
3. What is the probability of having a z-score that is between -1.27 to 1.06?
Finding Z-Scores from Areas
Answer the following questions based on the properties of standard normal distribution.
i) by Z table
ii) by calculator
1. Find the z-score that represents the bottom 70%.
2. Find the z-score that represent the top 70%.
3. Find the z-scores that represent the top 4% and the bottom 4%.