The plant manager wants to know what proptio of all batteries produced that day lasted less than 16 hours, which he has declared "unsuitable". From past experience, regarding 10% of batteries made at plant are unsuitable. If he can feel relativel certain that the proption of unsuitable batteries p produced that day is less than 0.10, he might take the chance of shipping the whole batch of batteries to customers.
1. Assuming that the actual proprtio of unsuitbale batteries produced that day is 0.10, what are the shape, center, and spread of the distribtuion of sample propptions for random samples of 480 batteries? Justify each of your answer
2. On this particular day a total of 480 batteries were tested during 16 hours of production. Forty of these batteries were unsuitbale. Calculate the proboalbity of obtaining a sample in which such a small probpotion of batteries is unsuitbale of p=0.10. SHow your work
3. Based on your answer to Question 5, what advice would you give the plant manager? Why?