Normal distribution and continuous random variable

Normal distribution and continuous random variable

Lessons

  • 1.

    \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

  • 2.
    Reading the Z Table
    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.


  • 3.
    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?


  • 4.
    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%.