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[solution]: 1. The management of a certain insurance company believes that


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1. The management of a certain insurance company believes that workers are more

 

productive if they are happy with their jobs. The company regularly conducts surveys, so

 

as to keep track of the satisfaction of their 815 workers. In a recent survey, the found out

 

that the mean job satisfaction score for all workers at the company was 13.25 (on a scale

 

of 1 to 20) and the standard deviation was 1.6. Assuming that the job satisfaction scores

 

of workers are normally distributed:

 

a. Calculate probability that a randomly selected worker will have a job satisfaction

 

score that is between 14 and 18.5? Interpret what your answer means.

 

b. A worker with a score of 9.0 or less is considered very unhappy with their job.

 

Give an approximate number of workers who are very unhappy with their jobs?

 

c. A worker with a score in the top 7% of scores is considered to be very happy

 

with his/her job. What is the minimum score needed to be considered very

 

happy? Round your answer to the nearest tenth. Which percentile have you just

 

found?

 

d. A worker in the company who has a score in the bottom 2.5% of scores is seen as

 

needing intensive job counseling with a job satisfaction score of ______ or

 

less. Fill in the blank.

 

2. Scores for a civil service exam are normally distributed and has variance of 47.61. To be

 

eligible for civil service employment, you have to score in the top 5%. If the lowest score

 

that you can earn and still be eligible for employment is an 84, what is the exam mean

 

score?

 


 

 


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