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 815 workers' satisfaction, the company regularly conducts surveys. According to a recent survey, the mean job satisfaction score for all workers at this company was 13.25 (on a scale of 1 to 20) and the standard deviation was 1.6. 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 and 18.5? Interpret the meaning of your answer.
b) A worker with a score of 9.0 or less is considered very unhappy with his/her job. Approximately how many workers 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 at this company with a score in the bottom 2.5% of scores is viewed as needing intensive job counseling with a job satisfaction score of ______ or less. Fill in the blank. Round to the nearest tenth.