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P11.1011 Statistical Methods for Public, Nonprofit, and Health Management

Homework – Class 3

1. Assume that the distribution of a college entrance exam is normal with a mean of 500 and a standard deviation of 100. For each score below, find the equivalent Z score, the percentage of the area above the score, and the percentage of the area below the score.

Xi

Z score

% Area Above

% Area Below

650

 

 

 

400

 

 

 

375

 

 

 

586

 

 

 

437

 

 

 

526

 

 

 

621

 

 

 

498

 

 

 

517

 

 

 

398

 

 

 


2. After taking the state merit examinations for the positions of social worker and employment counselor, you receive the following information on the tests and on your performance. Scores on both of the tests are normally distributed. On which of the tests did you do better?

 

Social Worker

Employment Counselor

 

 = 118

 = 17

Your score = 127

 

= 27

 = 3

Your score = 29

 

3. To be accepted into an honor society, students must have GPAs in the top 10% of the school. If GPAs are normally distributed and the mean GPA is 2.78 and the standard deviation is .33, which of the following GPAs would qualify? 3.20, 3.21, 3.25, 3.30, 3.35


4. Assume that you have lost your expired New York State drivers license and must go the Dept. of Motor Vehicles (DMV) office in person to get a new license. The office is near your workplace, and you hope to go during your lunch hour. Fortunately, you have a friend who works as a management analyst at the DMV. He informs you that they keep close track of the total time (waiting time plus processing time) that people spend for visits to the DMV. For transactions like yours, he tells you that the mean time is 20 minutes and the standard deviation for these times is nine minutes, and that wait times are approximately normally distributed.

  

a) What is the likelihood that you will be done with your business at the DMV in 15 minutes or less? Show your calculations and use a picture of the normal distribution to help. State the result of your conclusion in a clear, complete sentence.

 

Calculations Picture


Conclusion

 b) What is the likelihood that you will have to spend 30 minutes or more at the DMV? Show your calculations and use a picture of the normal distribution to help. State your conclusion in a clear, complete sentence.

 

Calculations Picture


Conclusion