Calculate the z-score for the following raw scores given a mean

Standardized Score In-Class Examples

1. Calculate the z-score for the following raw scores given a mean of 13.2 and a standard deviation of 2. After you have calculated that, please calculate the percent of score that fall below that given z-score.

Raw       Z-score Percent below

13.2                       

15.2                       

16.8                       

11.6                       

 

2. Calculate the z-score for the following raw scores given a mean of 13.2 and a standard deviation of 2. After you have calculated that, please calculate the percent of score that fall below that given z-score. However, a lower score is better in this instance, so you will need to adjust the formula.

Raw       Z-score Percent below

13.2                       

15.2                       

16.8                       

11.6                       

3. What percentage of data fall between a z-score of -1 and 1?

4. What percentage of data fall between a z score of -2.3 and 1?

5. What percentage of that data fall below a z-score of -2 and above 2?

6. What z-scores would 92% of the data fall between?

7. You are asked to develop a normative table for a newly developed test of aerobic fitness. Briefly, people run for 15 minutes and their total mileage is recorded as their score. The thought is the higher the mileage, the higher the aerobic fitness. You tested a huge population of individuals and found the mean mileage to be 1.6 miles with a standard deviation of 0.26. Fill in the raw scores in the table below that corresponds to the percentile.

Percentile           Raw Score

95th      

75th      

50th      

25th      

5th        

8. A country town installs 2000 new electric lights in a new housing estate. These lamps have an average life of 1000 hours with a standard deviation of 200 hours. Hint: Draw and label a normal “bell-shaped” curve to help answer this

a) What percentage of bulbs would be expected to fail between 800 hours and 1200 hours?

b) Howmany bulbs would this be?

c) How many bulbs would be expected to last longer than 1600 hours?