Sampling Distribution of the Sample Mean An orange juice producer buys all his oranges from a large orange grove that has one variety of orange. The amount of juice squeezed from these oranges has a mean of 4.70 ounces and a standard deviation of 0.60 ounces. After an early frost, the producer is concerned that the quality of the oranges has been compromised and that the amount of juice squeezed from each orange will decrease. A random sample of 45 oranges from the latest shipment is selected, and the average amount of juice squeezed from the sample of oranges is recorded. Identify what variable was recorded in this example. Is it a qualitative or quantitative variable? What conjecture has been made by the producer? Assuming the amount of juice squeezed from these oranges has not been affected by the early frost, completely describe the sample mean amount of juice squeezed from a sample of 45 oranges The sample of 45 oranges had an average 4.62 ounces of juice. Assuming the early frost has not affected juice amounts, what is the probability of observing a sample mean of 4.62 ounces or less? Based on the probability found above, what (if anything) can be inferred about the mean amount of juice squeezed from the oranges after the early frost?52. Rainfall Statistics from Cornell's Northeast Regional Climate Center indicate that Ithaca, New York, gets an average of 35.4" of rain each year, with a standard deviation of 4.2". Assume that a Normal model applies. a) During what percentage of years does Ithaca get more than 40" of rain? b) Less than how much rain falls in the driest 20% of all years? c) A Cornell University student is in Ithaca for 4 years. Let y represent the mean amount of rain for those 4 years. Describe the sampling distribution model of this sample mean, y. d) What's the probability that those 4 years average less than 30" of rain