Question 1 :

The management of a large insurance company believes that workers are more productive if they are happy with their jobs. To keep track of their 2500 workers' satisfaction, the company regularly conducts surveys. According to a recent survey, the mean job satisfaction score for all workers at this company was 14 (on a scale of 1 to 20) and the standard deviation was 2. Assume that the job satisfaction scores of workers are normally distributed.

a) What is the probability that a randomly selected worker will have a job satisfaction score between 14.5 and 18.5? Report your answer to 3 decimal places.

b) A worker with a score of 9.75 or less is considered very unhappy with their job. What is the probability that a worker is very unhappy with their job? Report your answer to 3 decimal places.

c) A worker with a score of 9.75 or less is considered very unhappy with their job. Approximately how many workers are very unhappy with their jobs? Report your answer to the nearest whole person.

c) A worker with a score in the top 10% of scores is considered to be very happy with their job. What is the minimum score needed to be considered very happy? Round your answer to the nearest tenth.

d) A worker with a score in the top 10% of scores is considered to be very happy with their job. What percentile is this?