z-scores

Hand in your answers and your work. Please report and label all your answers clearly

and show your work as neatly as possible!

For all the homework questions, we will use Openness to Experience scores - higher scores indicate higher degrees of openness to experience.

"People with high levels of openness are more likely to seek out a variety of experiences, be comfortable with the unfamiliar, and pay attention to their inner feelings more than those who are less open to novelty. They tend to exhibit high levels of curiosity and often enjoy being surprised. People with low levels of openness prefer familiar routines, people, and ideas" (Psychology Today)

Use these parameters for all questions: = 58, = 9

Part 1.

Draw the distribution for Openness to experience scores based on the mean and standard deviation of the population. Under the X-axis, write the symbols for the parameters, the Openness to experience scores and the z-scores up to 3.

Part 2

Questions

1. What proportion of people has Openness scores greater than 68?

2. What proportion of people has Openness scores below 38?

3. In a sample of 200 people, how many would be expected to have Openness scores below 45?

4. In a group of 30 people, how many would be expected to have Openness scores above 60?

5. What openness score marks the top 10% of Openness?

6. What proportion of people have Openness scores between 48 and 66?

7. What proportion of people have Openness scores between 75 and 85?

8. Find the Openness scores that separate the middle 95% of scores from the extreme 5%.

9. Find the Openness scores that separate the middle 99% of scores from the extreme 1%.