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 2741 workers' satisfaction, the company regularly conducts surveys.According to a recent survey, the mean job satisfaction score for all workers at this company was 14.25 (on a scale of 1 to 20) and the standard deviation was 1.75.Assume that the job satisfaction scores of workers are normally distributed.

a.What is the probability,rounded to the nearest thousandth (3decimal places), that a randomly selected worker will have a job satisfaction score between 14.5 and 18.5?

b. A worker with a score of 9.25 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 15% of scores is considered to be very happy with his/her job.(i) What is the minimum score needed to be considered very happy?Round your answer to the nearest tenth.(ii) Which percentile have you just found?