20.5. Solving Problems Involving Normal Distribution

Try these first

1. 1.

   Identify the mean and standard deviation if the data is: Mean = 50, Standard Deviation = 5.

   Hint

   Look at the parameters given directly.

2. 2.

   Convert a raw score of 90 to a Z-score if the mean is 80 and standard deviation is 10.

   Hint

   Use the Z-score formula when given X, mean, and standard deviation.

3. 3.

   What does the Z-score tell you?

   • Mean of the distribution
   • Standard deviation
   • How many standard deviations a score is from the mean

   Hint

   Remember, Z-scores help in standardizing various scores.

4. 4.

   True or False: The total area under the normal distribution curve is equal to 2.

   • True
   • False

   Hint

   Visualize the curve; it reflects total probability.

5. 5.

   A factory's defect rate is normally distributed with a mean of 3 defects per 1000 units and a standard deviation of 1 defect. Find the probability that out of 1000 units, the defects will be fewer than 1.

   Hint

   Always convert raw scores to Z-scores before looking up the tables.

6. 6.

   In a population with a mean of 160 cm and a standard deviation of 20 cm, find the height at which 90% of individuals are below.

   Hint

   Look up the correct area in the Z-table and backtrack to find the raw data score.