Statitics question

Question

Researchers are interested in the stress levels of various working professionals. Systolic Blood pressure, alcohol consumption, and the Standard Stress Inventory (SSI) can all used as indicators of stress. Calculate z score for each of the following:

           

            a) The president of a major company has a systolic blood pressure reading of 150, and in  the US population the systolic blood pressure is 110 with a standard deviation of 12.

 

 

 

            b) On average people in the US consume 5 alcoholic beverages a week with a standard          deviation of 3.7 Joe the local stock trader consumes 16 alcoholic beverages a week.

 

 

            c) DePaul students have an average SSI rating of 15 and a standard deviation of 3. Your    roommate’s  SSI rating is 7.

 

 

Which of these men is the most stressed out? Why/ how do you know?

 

 

Which is the least stressed out? Why/ how do you know?

 

 

Who is the furthest away from the mean?

 

 

 
 

 

 

 

 

Answer 1

hi Jennifer!

 

Recall that z score = # of standard deviations away from the mean (keeping track of sign).

 

Once you have the mean, the standard deviation and the value, you can easily compute z.

 

For the first z = (150-110)/12 = 3.33

For the second z = (16-5)/3.7 = 2.97

For the third z = (7-15)/3 = -2.67

 

Assuming each indicator is positively correlated with stress and that they are of equal importance, the first man is most stressed out since the z score is the highest.

 

By the same reasoning, the third man who has the lowest z-score is least stressed out.

 

The first man is furthest away from the mean in terms of z-score.

 

Answer 2

Hi Jennifer,

 

I've repeated the complete question below as it's easier to organize the answers this way.

 

Researchers are interested in the stress levels of various working professionals. Systolic Blood pressure, alcohol consumption, and the Standard Stress Inventory (SSI) can all used as indicators of stress. Calculate z score for each of the following:

a) The president of a major company has a systolic blood pressure reading of 150, and in the US population the systolic blood pressure is 110 with a standard deviation of 12.


Z = (X-μ)/σ

Where μ =  mean

σ = standard deviation

 

Z = (150-110)/12 

Z = 40/12

Z = 3.333


b) On average people in the US consume 5 alcoholic beverages a week with a standard deviation of 3.7 Joe the local stock trader consumes 16 alcoholic beverages a week.

Z = (16-5)/3.7 
Z = 11/3.7
Z = 2.973

c) DePaul students have an average SSI rating of 15 and a standard deviation of 3. Your roommate’s SSI rating is 7.

Z = (7-15)/3 
Z = -8/3
Z = -2.667


Which of these men is the most stressed out? Why/ how do you know?

 

The greater the absolute value of the Z score, the further away from the mean as a percent of standard deviation.  The man with 150 systolic blood pressure is the most stressed out.


Which is the least stressed out? Why/ how do you know?

Using the logic above, the person with the smaller absolute value of Z would be the least stressed out.  This would be the DePaul student.


Who is the furthest away from the mean?

 

The president is 3.333 standard deviations away from the mean.