20.6. Example Problems

Try these first

1. 1.

   What is the Z-score for a value of 90 when the mean is 75 and standard deviation is 5?

   Hint

   Use the Z-score formula: Z = (X - μ) / σ.

2. 2.

   If the mean is 50 and standard deviation is 10, what is the probability of scoring below the mean?

   Hint

   Consider the properties of normal distribution.

3. 3.

   What is the mean in the Normal Distribution?

   • Mode
   • Median
   • Average

   Hint

   Consider what the term 'mean' refers to in statistics.

4. 4.

   Z-scores can only be positive.

   • True
   • False

   Hint

   Think about how Z-scores are calculated.

5. 5.

   Given a mean of 50 and standard deviation of 5, find the probability of obtaining a score greater than 60.

   Hint

   Calculate the Z-score and refer to the Z-table.

6. 6.

   Determine the range for which 95% of the data lies in a normal distribution with a mean of 200 and standard deviation of 30.

   Hint

   Recall the Empirical Rule.