A cosmetic manufacturer is interesting in estimating the actual amount of shampoo that is placed in a 200 ml bottle to ensure that they are not over-filling or under-filling the bottles. The manager of the bottling plant took a random sample of 100 bottles and calculated the mean to be 199ml with a standard deviation of 0.90.

1. Set up a 95% confidence interval of the true population mean amount of shampoo in each bottle.

2. Interpret this confidence interval in relation to the situation.

3. Does the bottling plant need an adjustment (explain)?