In the past year, 15% of all garments made in a factory had a defect of some kind. To reduce the proportion of defective garments, the factory manager offers a $100 bonus for each employee if she fins convincing evidence that the proportion of defective garments produced during the next month is less than 0.15. At the end of the month, the manager selects a random sample of 200garments and finds that 26 of them have a defect.

a) Draw a picture of the sampling distribution of the sample proportion of defective garments for random samples of size 200. Label appropriate values and justify your reasoning for its shape.

b) Calculate the probability of getting a sample proportion of defective garments of 26/200 or less. Show work.

c) Based on your previous answers, is there convincing evidence that the proportion of garments produced this month with defects is less than 0.15? Eplain