20.3. Standard Normal Distribution

Try these first

1. 1.

   What is the Z-score for a value of 50 with a mean of 50 and a standard deviation of 10?

   Hint

   Think about how many standard deviations away it is from the mean.

2. 2.

   If X = 60, μ = 50, and σ = 5, what is the Z-score?

   Hint

   Subtract the mean and then divide by the standard deviation.

3. 3.

   What is the mean of the Standard Normal Distribution?

   • 0
   • 1
   • Any real number

   Hint

   Remember, all values are standardized!

4. 4.

   True or False: The standard deviation of the Standard Normal Distribution is 1.

   • True
   • False

   Hint

   Think about the standardization process!

5. 5.

   A distribution has μ = 100 and σ = 15. Calculate the Z-score for a value of 130 and the associated probability.

   Hint

   Start with the Z-score formula, then use the table to find the area.

6. 6.

   In a sample of test scores with μ = 50 and σ = 5, what is the probability that a score is lower than 48?

   Hint

   Know how to interpret the negative Z-scores in the table.