Navel oranges contain an average of 60ml of juice, with a standard deviation of about 30ml. Taylor, an agricultural researcher, will squeeze a sample of 36 of the oranges. (a) Describe the sampling distribution of the sample average ¯x of the juice contents. (mean and standard deviation)
(b) Within what interval would you expect the sample average to lie, with probability 0.9?
(c) Calculate the probability with which the sample mean ¯x is less than 57.5 ml.
(d) After the experiment, Taylor would like to make mimosas to share with her colleagues. If the recipe calls for a total of 2.25 liters of orange juice, what is the probability that Taylor will have enough juice to follow the recipe?