Question

In the past year James has moved to a new state, changed jobs, and experienced the end of a relationship. The Holmes and Rahe Stress Scale (HRSS) is used to assess one's cumulative stress in the past year and this score (1-600) is used to assess their risk for developing some sort of mental health condition. The mean score is 250 with a standard deviation of 20. James completes the HRSS and receives a score of 294.

3. Calculate James' z-score and determine what percent of scores in the population distribution are higher than his? Hint: You will need to refer to the normal curve table in the appendix of your textbook.

4. If James were to score in the top 50 percent of all individuals completing the HRSS what would his minimum raw score on the questionnaire need to be? Hint: You will need to refer to the normal curve table in the appendix of your textbook.

Answer 1

Solution :

Given that ,

mean = = 250

standard deviation =  = 20

3) x = 294

Using z-score formula,

z = x - /   

z = 294 - 250 / 20

z = 2.20

Using standard normal table,  

P(Z > 2.20)

= 1 - P( Z < 2.20)

= 1 - 0.9861

= 0.0139

4) Using standard normal table,

P(Z > z) = 50%

= 1 - P(Z < z) = 0.50  

= P(Z < z) = 1 - 0.50

= P(Z < z ) = 0.50

= P(Z < 0 ) = 0.50  

z = 0

Using z-score formula,

x = z * +

x = 0 * 20 + 250

x = 250

minimum raw score = 250